Theory Group at Dep. Phys. "Enrico Fermi"

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Theory Group at Dep. Phys. "Enrico Fermi"
Congressino Dip Fis 11/4/2011

             Theory Group at Dep. Phys. “Enrico Fermi”
                 •        “Theories of the fundamental interactions towards 2020”
                      D. Anselmi, A. Strumia, L. Bracci, G. Cicogna, F. Bigazzi, E. Meggiolaro,
                      G. Paffuti, C. Giannessi, S. Servadio, P. Christillen, K. Konishi;
                      A. Di Giacomo, L. Picasso, T. Elze, G. Morchio, E. D’Emilio, T. Fujimori, Y. Jiang,
                      M. Cipriani, A. Michelini, D. Dorigoni, S. Giacomelli, M. Taiuti, E. Ciuffoli,
                      C. Bonati, R. Torre, P. Giardino,

                 •        “A survey of quantum field theory and applications”
                          E. Vicari, P. Rossi, E. Guadagnini, M. Campostrini, M.Mintchev,
                          B. Alles, P. Calabrese;
                          P. Menotti, C. Torrero, G. Paoletti, G. Ceccarelli, E. Profumo, M. Fagotti

                •     “Theoretical nuclear physics”
                          I. Bombaci, A. Bonaccorso, M. Viviani, A. Kievsky, L. Marcucci;
                          S. Rosati, R. Kumar
                                                                                                The Speakers

Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Fundamental Problems in Physics Today
    Three “melodies” of the 20th C Theoretical Physics: (C.N.Yang 2002)                    Anomaly
                                                                                           cancellations !
      “Quantization, Symmetries and Phase Factors”
                                                          “Standard Model” of the fundamental interactions
   Local, renormalizable gauge theory
      (of pointlike objects - the elementary particles)
                                                              ➩         SU(3)QCD x (SU(2)xU(1))GWS
                                                                        Quant. chromodynamics   Glashow-Weinberg-Salam’s
                                                                                                                         ’70-’74

                                                                        Nuclear forces          Electroweak theory
                                                                                     Orig
  BUT !!                  Why MW / MPlanck ~
                          “naturalness/hierarchy” problem
                                                         10-17
                                                                               η pr
                                                                                    mas in of
                                                                                   oble
                                                                                         s?
                                                                                                               mν ≪
                                                                                                              ≪ m me , mu
                                                                                                                  c ≪
                                                                                        m   ?                         mt ?
   • Higgs? Supersymmetry ? GUTS?                                                           Origin of
   • Quantum gravity? Black-hole entropy?
                                                                 LHC             μ problem? the universe?            ν?
  •    New principles? New paradigm? Holographic principle?                                     AdS/CFT?         Maldacena ’97
       ◦ String theory?
        ◦ Lorentz Invariance Violation at short distances?
                                                                                      BIG BANG / Inflation
        ◦ Susy breaking? Extra dimensions?
                                                                         Standard                   Observational Cosmology
 • Cosmology                                                            Cosmology                   and Astroparticle physics
                              Ωm =0.26±0.02; ΩΛ =0.74±0.02; Ωb =0.04;

         dark matter? dark energy? GRB, UHECR                                                       COBE, WMAP, SDSS, ...

 • Quark Confinement (non-Abelian strong gauge dynamics) ?                                          FERMI/LAT , AMS...
         σtot ∿ log2 s    ?    Quark-gluon plasma, Color superconductivity?
  • Quantum mechanics : fundamental aspects. Time? Schrödinger’s cat
                                                                                                 Pn = |!n|ψ"|2 ?
                                                                                           Entanglement/Quantum computing
      We are perhaps at the pre-dawn of a new scientific revolution
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
This presentation
                                       Damiano
                                                        Enrico
                          Alessandro
                                                         Adriano and Com.

                                                                 Thomas

                                                   Luc, Lui, Giam

                                              Gianni

                                       Francesco (B):

                               Ken & Com.

                                   Daniele

                                  Giampiero & Ken

                                         END
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
arXiv:1012.4515 and 1009.0224
      We found that electroweak corrections are relevant if DM is heavier than the
      weak scale, and included them in a public code.

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                          We provide ingredients and recipes for computing signals of TeV-scale
                             Dark Matter annihilations and decays in the Galaxy and beyond.

Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Lorentz violating renormalizable Standard Model
                                                         Damiano Anselmi
                          + Emilio Ciuffoli, Martina Taiuti and now Dario Buttazzo and Diego Redigolo

   Idea: use the violation of Lorentz symmetry to renormalize interactions
                    that are normally nonrenormalizable

   Higher powers of momenta in dispersion relations and propagators make the
           integrands of Feynman diagrams more convergent in the UV

   A modified power counting criterion, which assigns different weights to space and
           time, controls the UV behavior and the renormalizability of the theory

   Apart from violating Lorentz symmetry, the theory remains renormalizable, local,
           polynomial, unitary and causal (with causality defined according to
      Bogoliubov,, which only needs past and future, no light cones)

   No counterterms with higher time derivatives are generated by renormalization, so
          (perturbative) unitarity is safe

   Since the purpose is to cure the UV behavior of otherwise nonrenormalizable
           interactions, Lorentz symmetry can be recovered in the IR by a fine tuning
           of parameters. It is possible to have agreement with data
Tuesday, April 12, 2011
Theory Group at Dep. Phys. "Enrico Fermi"
Consider the free theory (a hat denotes time,
                                                   time a bar denotes space)

           Its propagator is

           and the dispersion relation reads

          The improved ultraviolet behavior allows us to renormalize otherwise non-
                                                                               non

          renormalizable vertices. They can be classified using a weighted power counting
Tuesday, April 12, 2011
An example of nonrenormalizable vertex that becomes renormalizable is

       which gives neutrinos Majorana masses after symmetry breaking.

       Other examples are the four-fermion vertices

       at the fundamental level.

       Four-fermion vertices are bounded by existing limits on proton decay.

       Both vertices are compatible with a scale of Lorentz violation

                                                                        (10-28 - 10-29 cm )

       which agrees with present data (possibly apart from the still mysterious ultrahigh-
       energy cosmic rays), if Lorentz symmetry is violated but CPT is preserved (or
       broken at much larger energies)
Tuesday, April 12, 2011
We can build a Standard Model extension without elementary scalars

   where

     The model contains four fermion interactions at the fundamental level. It is possible to
     describe the known low-energy
                            energy physics in the Nambu—Jona-Lasinio spirit, which gives
     masses to fermions and gauge bosons dynamically. The Higgs field is a composite
     field and arises as a low-energy effect

     An interesting low-energy
                        energy prediction is the formula

     which is in perfect agreement with data for

Tuesday, April 12, 2011
Summary of research topics and recent papers

                      Formulation of Lorentz Violating Stardard Model (LVSM):
               D.A., Weighted power counting, neutrino masses and Lorentz violating extensions of
                   the Standard Model, Phys.. Rev. D 79 (2009) 025017 and arXiv:0808.3475 [hep-ph]

                      Scalarless LVSM and its phenomenology:
                      I build a version with no fundamental scalar and analyse its phenomenology

               D.A., Standard Model Without Elementary Scalars And High Energy Lorentz Violation,
                                                                                       Violation Eur.
                   Phys. J. C 65 (2010) 523 and arXiv:0904.1849 [hep-ph]
                                                                [

                      Detailed analysis of low-energy phenomenology of scalarless LVSM:
                      We show that we can find agreement with all data, within theoretical errors

               D.A. and E. Ciuffoli, Low-energy
                                         energy phenomenology of scalarless Standard Model extensions
                   with high-energy Lorentz violation, Phys. Rev. D 83 (2011) 056005 and
                   arXiv:1101.2014 [hep-ph]

                      Experimental limits and theoretical analysis on the scale of Lorentz violation:
                      Here we show that                              is consistent with all data (at preserved CPT).
                      We claim that in Nature Lorentz symmetry may be broken well below the Planck scale

               D.A. and M. Taiuti, Vacuum Cherenkov radiation in quantum electrodynamics with high-
                   energy Lorentz violation, PRD in print and arXiv:1101.2019 [hep-ph]
                                                                              [

Tuesday, April 12, 2011
Attività di ricerca di ENRICO MEGGIOLARO
        Diffusione “soffice” ad alta energia in QCD

               Diffusione “soffice” ad alta energia in QCD
               Usando un approccio basato sull’integrale funzionale, le ampiezze
               di diffusione elastica adrone–adrone (e.g.,! mesone–mesone), ad
                             √
               alta energia ( s " 1 GeV) e “soffici” ( |t| ! 1 GeV), vengono
               ricostruite da certe funzioni di correlazione di due “loop di Wilson”
               nello spazio–tempo di Minkowski (ampiezze dipolo–dipolo).

Tuesday, April 12, 2011
Attività di ricerca di ENRICO MEGGIOLARO
       Diffusione “soffice” ad alta energia in QCD

               In [M. Giordano, E. Meggiolaro, Phys. Rev. D 78 (2008) 074510;
               Phys. Rev. D 81 (2010) 074022] il problema è stato affrontato
               (per la prima volta) dal punto di vista della QCD su reticolo,
               mediante un calcolo diretto (utilizzando l’infrastruttura GRID
               dell’I.N.F.N.), con simulazioni Monte Carlo nella teoria di pura
               gauge SU(3), della funzione di correlazione Euclidea di due
               loop di Wilson, da cui l’ampiezza di diffusione mesone–mesone può
               essere ricostruita mediante continuazione analitica.
               [M. Giordano, E. Meggiolaro, Phys. Lett. B 675 (2009) 123-132;
               M. Giordano, Tesi di Dottorato, Pisa, 20/10/2009; relatore: E. M.]

               Questo è attualmente l’UNICO approccio al problema della
                                       ------------------
               diffusione “soffice” adrone–adrone ad alta energia da principi primi
               (QCD) e non–perturbativo.
                                                                  ----------------
               --------------------------
               =⇒ I modelli analitici testati (SVM, ILM, AdS/CFT) risultano
               insoddisfacenti. Si cercano nuove forme funzionali che fittino
               meglio i dati su reticolo . . .
Tuesday, April 12, 2011
Attività di ricerca di ENRICO MEGGIOLARO
       Diffusione “soffice” ad alta energia in QCD

               [E. Meggiolaro, M. Giordano, “High–energy hadron–hadron
               (dipole–dipole) scattering on the lattice”; E–print: arXiv:1010.0914
               [hep–lat]; presentato da E. Meggiolaro al simposio della conferenza
               HESI 2010, 10–13 agosto 2010, Kyoto, Giappone.]

               . . . La speranza è quella di riuscire a spiegare il comportamento
               (universale?) ad alta energia delle sezioni d’urto adrone–adrone
               a partire dall’ampiezza (fondamentale) dipolo–dipolo, calcolata
               nell’Euclideo: alcuni risultati preliminari sembrano condurre a
               σtot (s) ∼ (ln s)2 , in accordo coi dati sperimentali (e con il
               limite di Froissart) . . . [Work in progress]
Tuesday, April 12, 2011
Attività di ricerca di ENRICO MEGGIOLARO
      Simmetrie chirali e topologia in QCD (anche per T > 0)

             Simmetrie chirali e topologia in QCD (anche per T > 0)
              Si studia un modello di Lagrangiana Chirale Efficace che include
              (oltre all’usuale condensato chirale !q̄q" e all’anomalia) anche un
              certo condensato U(1) assiale (irriducibile) del tipo:

              CU(1) ∼ ![det(q̄sR qtL ) + det(q̄sL qtR )]",
                            st                     st

              che agisce come parametro d’ordine per la sola simmetria U(1)
              assiale e resta diverso da zero attraverso la transizione chirale a
              Tch $ 170 MeV, fino a una certa temperatura TU(1) > Tch .
              =⇒ implicazioni fenomenologiche, per esempio (per T < Tch ):
              i) nei decadimenti radiativi η, η ! → γγ
              [M. Marchi, E. Meggiolaro, Nucl. Phys. B 665 (2003) 425;
              E. Meggiolaro, Phys. Rev. D 69 (2004) 074017.]
              ii) nei decadimenti forti η, η ! → 3π, η ! → ηππ
              [E. Meggiolaro, E–print: arXiv:1010.1140 [hep–ph]; Phys. Rev. D
              (2011), in stampa.]
Tuesday, April 12, 2011
Confinement in QCD
                          nonperturbative methods on and off the lattice
       People
       Pisa: C. Bonati, A. Di Giacomo
       Active collaboration: M. D’Elia, P. Incardona (Genova),
       F. Sanfilippo (Roma), G. Cossu (KEK, Japan)
       Starting collaboration: APE group (Roma), M. Caselle (Torino)
                                Main interests and recent works:
          Mechanism of color confinement            Nucl. Phys. B 828, 390 (2010),
          vacuum dual superconductivity             Phys. Rev. D 81, 085022 (2010),
          through monopole condensation             Phys. Rev. D 82, 094509 (2010),
                                                    JHEP 0907, 048 (2009),
          QCD phase diagram
                                                    Phys. Rev. D. 82 114515 (2010),
          critical points & universality            arXiv:1011.4515 [hep-lat]
          classes                                   (accepted in PRD)

Tuesday, April 12, 2011
Dual superconductivity & monopoles
                      Continuum                                                                  Lattice
                      The gauge independence of                                                    !   The gauge dependence of the
                      the monopole definition was
                                                                                                       monopole detection was
                      established.
                                                                            3
                                                                                                       clarified.
                                         SU(2) gauge theory 4xNs
                                              Wu-Yang monopole of chage 4                          !   A revised version of the
                       0.01                                                                            monopole operator was
                         0                                                                             introduced.
          ~ )/N 1/"

                      -0.01
               s

                                                                                                  1. The problems of the previous
           b

                                                                                Ns=16
        ~-#

                      -0.02                                                     Ns=20
                                                                                                     implementation are solved.
       (#

                                                                                Ns=24

                      -0.03
                                                                                                  2. Good scaling at deconfinement
                      -0.04
                                                                                                     transition.
                              -6   -4    -2         0        2        4         6       8   10
                                                           1/"
                                                    (!-!c)Ns

                                        Perspectives: the revised order parameter can now be
                                        used to investigate confinement in real QCD and in
                                        other confining theories (e.g. G2 gauge theory)

Tuesday, April 12, 2011
QCD phase diagram

                     Nf = 2 chiral transition

              ∞                                          Study of the structure of the QCD phase
                    O(4)
               T
                                             1st         diagram at finite temperature and density,
                                        Z2
                                                         with particular emphasis on those aspects
                                cr
                                   o
                                  sso

                           Z2
                                                         of the phase diagram related to known
                                       ve

             ms
                                       r

                     1st
                                                         symmetries of QCD (i.e. chiral symmetry)
                0                 mu               ∞

                Main focus: determination of the order Nf = 2 chiral transition.
                Previous studies of the group, Phys. Rev. D 72, 114510 (2005),
                indicated the first order nature of the transition, which is usually
                                      believed to be 2nd order.
                             Huge computational resources needed!

Tuesday, April 12, 2011
Computational tools
              The video game market developments compelled graphic cards
                 manufacturers to increase the floating point calculation
                  performance of their products ⇒ New architecture for
                computations: Graphic Processing Units (GPUs)

         Need to rewrite all codes and some care is needed in optimizations
         (see arXiv:1010.5433) but TOTALLY WORTH IT!

                                 With our current implementation
                                1 GPU ⇐⇒ 1 − 3 apeNEXT crates
                      possible present alternatives (e.g. CPU clusters) lose a
                           factor 3 in price and 6 in power consumption

         Ongoing developments:
          ! (short-term) parallelize the work between several GPUs
            (in collaboration with the APE group)
          ! (long-term) fermions with improved chiral properties
            (still more computationally demanding!)

Tuesday, April 12, 2011
Tuesday, April 12, 2011
Tuesday, April 12, 2011
---------------------------

Tuesday, April 12, 2011
L. Bracci e L. E. Picasso: rappresentazioni algebra di
             Weyl
                                      !                         !
             In Rn : U (α) ≡ e−i αip̂i V (β) ≡ e−i βiq̂i , U (α)V (β) = eiα·β V (β)U (α)
             von Neumann: RI equivalenti; rappres. completamente riducibili.

               Spazio semilimitato U (α) semigruppo isometrie, V (β) gruppo ⇒
             σ(q̂) = [x0, ∞), R I con dato x0 equivalenti1. Z ≡ Centro = {λI} ⇒
             H = ⊕iHi, Hi irriducibili, stesso x0. σ(q̂) è omogeneo in [x0, ∞) 4.
             In generale: integrale di Hi con diversi x0 4.
             Irriducibilità ⇔ irrid. rispetto agli U (α) 1. L’algebra per R, per spazio
             semilimitato e quella generata da {U (α)} sono identiche 5.

              Segmento U (α) isometrie parziali, U (0) = I, U (1) = 0 ⇒
            σ(q̂) = [x0, x0 + 1], RI con lo stesso x0 equivalenti 1,3.
            Z = {λI}
                  {λI} ⇒     rappresentazioni completamente
                        ⇒ rappresentazioni                         riducibili33. .
                                               completamenteriducibili
            Se U!! (α),  !! (n)
                   (α), VV  (n) unitari
                                 unitari che
                                         che obbediscono
                                             obbediscono Weyl,
                                                            Weyl, perper RI RIèèU!(1)
                                                                                  !U       eiφ
                                                                                     (1)==eiφ I.I.
               con dato
            RI con   dato φφ sono
                                sono equivalenti.
                                      equivalenti. Se
                                                   Se U!(1)
                                                      !U    =eeiφiφII èèZZ=
                                                         (1)=                    {λI}33. .
                                                                             ={λI}

              Sfera
               Sfera Algebra
                         Algebra A   A generata
                                        generata da    da $n ee J$J$ èè EE33 (gruppo
                                                          n$                    (gruppo euclideo
                                                                                          euclideo3-dim.)
                                                                                                     3-dim.)
            Le RIRI sonosono le
                              le RIRI (l
                                       (l00,,0)
                                              0) di   so(3,1).
                                                  di so(3,           Casimir J$J$· ·$
                                                             1). Casimir              n ≡≡σσ ==±l
                                                                                     n$           ±l
                                                                                                   00. . AAèè
            sottoalgebra
            sottoalgebra di    di A ASS generata
                                        generata da    da $    $L,
                                                           n,, L,
                                                          n$       $S,
                                                                $ S, $ ⇒   ⇒perperparticella
                                                                                   particelladidispin
                                                                                                  spinS, S,HH
            irriducibile
            irriducibile sotto
                            sotto A  ASS,, èè H
                                                H= =⊕ ⊕σ=S
                                                         σ=S H      , H sede della RI (|σ|, 0) di A
                                                         σ=−S Hσσ , Hσσ sede della RI (|σ|, 0) di A
                                                        σ=−S
            con JJ$$ ·· $
                        n=
                        n
                        $ = σσ 66..

Tuesday, April 12, 2011
Spazio non semplicemente connesso RI non equivalenti. Nel piano
          bucato, {$               q , −i∇ + f$($
                       q , −i∇} e {$            r)}, ∇ ∧ f$ = 0, non equivalenti se
          "
              $ r) · d$
            γ f ($    r '= 0 ⇒ re-interpretazione effetto Aharonov-Bohm: H =
                    $2
                    p
          Hlibera = 2m , ma
                                  Φ             !
                      ! r), f = 2π!r2 (−x2, x1), γ f!d!
           ! = −i∇ + f (!
           p                !                         r=Φ .
           Φ #= 2nπ ⇒ effetto Aharonov-Bohm. Quindi A-B segue dall’esistenza
           di RI non equivalenti. È l’osservazione che determina quale Φ (quale
           rappresentazione) scegliere 2.

           1)   Journal Math. Phys. 47 112102 (2006)
           2)   American J. Phys. 75 268 (2007)
           3)   Bull. London Math. Soc. 39 791 (2007)
           4)   Lett. Math. Phys. 89 277 (2009)
           5)   Lett. Math. Phys. 93 267 (2010)
           6)   Eur. Phys. J. Plus 126 4 (2011l

    G. Cicogna:
    Studio analitico e algebrico di equazioni differenziali non lineari di interesse fisico.
    Speciale attenzione e' dedicata alla introduzione di opportune generalizzazioni
    della nozione di algebra di Lie delle simmetrie. Le applicazioni includono:
    problemi nella fisica dei plasmi, fenomeni di biforcazione, comparsa di soluzioni
    periodiche e/o complesse, tecniche di riduzione e di integrazione, leggi di conservazione
    generalizzate.

Tuesday, April 12, 2011
1. Algebre di Poisson non commutative, invarianza per diffeomorfismi e
           quantizzazione
           Risultati:
            A) MQ sulle varietà differenziabili                                            More about it
            B) Derivazione della quantizzazione di Dirac senza inconsistenze

           2. Estensione delle previsioni della MQ e dise-
           guaglianze di Boole-Bell

          3. La matrice di scattering in QED: esistenza,
          costruzione non perturbativa. Possibile costruzione dei campi carichi asintoti-
          ci attraverso correzioni di stringa che superano lʼostruzione data dallʼassenza di
          stati carichi a massa definita.

          4. Risultati esatti su identità di Ward, topologia e simmetria chirale in QCD:

Tuesday, April 12, 2011
Progetti:
           - Gradi di libertà interni e diffeomorfismi
           - Covarianza e invarianza per diffeomorfisimi in gravità quantistica
           - Possibilità di una descrizione completa di matrice S in QED via LSZ modificato
           - Implicazioni dei modelli e della costruzione LSZ generalizzata sulla localizzabilit`a e la
           classificazione degli stati carichi in QED
           - Implicazioni della struttura delle osservabili locali sulle identit`a di Ward del problema
           U(1) e sul problema CP forte
           - Parametri e gerarchie di massa in supercon-
           duttivit`a oltre il BCS

Tuesday, April 12, 2011
3(1*-/'-)&M4+1NN4 >OH3H?
  !"#$%&'()*
  !"#$%&'"()*+,%&-)#.,/$&0#1*"#2&34/,$&56/)(4/'&7%&2/1*'&)8&&6),)+(1.64-&$#1,'9&
  4:/:&;/1-)*84*/2/*"9&21''&+1.9&F#1(
Tuesday, April 12, 2011
K. Konishi and
                                      Fujimori, Jiang, Dorigoni,
                                    Michelini, Giacomelli, Cipriani
                              + Carlino, Murayama, Spanu, Grena, Auzzi,Yung, Bolognesi,
                     Ferretti, Nitta, Ookouchi, Ohashi,Yokoi, Marmorini, Vinci, Eto, Gudnason, Evslin
                                (Armenia-Italy-Japan-USA-Russia-Denmark-China Collaboration)

       • Nonabelian vortices:          (non-Abelian monopoles and confinement )                                  ’03-’11

       • “Almost conformal” vacua for confinement                                 Auzzi, Grena, Konishi, ’03    Giacomelli

                                                                                                 Evslin, Giacomelli
        • Faddeev-Niemi decomposition for Yang-Mills theories                                             +             ’10-’11
                                                                                                 Michelini, Konishi

        • Large N, dimensionally reduced SU(N) SYM                                               Dorigoni, Veneziano,
                                                                                                      Wosiek
                                                                                                                           ’10

Tuesday, April 12, 2011
Nonabelian vortex, monopole and quark confinement
             • Dirac’s quantization condition      ( ’31 -- But he no longer believed it ’80)        e · g = n/2,      n= ±1,±2,...
             • Vortex in Landau-Ginzburg theory         (Abrikosov ’52,        Nielsen, Olesen’74)

             • ’t Hooft-Polyakov monopoles             (’74)                                               GUT? ➟ Inflation
             • Confinement by monopole condensation (dual Meissner effect)                                    (Mandelstam, ‘t Hooft ’80)

                                              But no evidence of dynamical abelianization
                                                                                                                    Seiberg-Witten
                                                                                                                     exact solns N=2
 • Nonabelian monopoles? Quantum mechanical nonabelian monopoles do appear                                                  ’94
   in N=2 susy theories (Carlino, Konishi, Murayama, 2000)

 • Nonabelian vortices: discovered by the Pisa group in 2003
                                                                                                                            ’03-’11
       ➪ Rich and deep physics results                                                                                        Pisa,
                                                                                                                          Minnesota,
                ◦ 4D gauge dynamics = 2D sigma model                                                                      Cambridge,
                                                                                                                            Tokyo,
                ◦ Vortex effective world sheet action   ➭    GNO duality                                                      ... ...
                ◦ Vortices in high-density QCD; multicomponent superconductivity
               ◦ Fractional vortices
               ◦ Role of the Global symmetry in dual gauge group
                                                                                                         Attracting the interest of
               ◦ Monopole-vortex complex soliton                                                         mathematics communitiy

Tuesday, April 12, 2011
Some References
            S.B. Gudnason, Y. Jiang, K. Konishi,
            "Non-Abelian vortex dynamics: Effective world-sheet action".
            JHEP 1008:012, 2010. (2010) e-Print: arXiv:1007.2116 [hep-th].

            M. Eto, T. Fujimori, S.B. Gudnason, Y. Jiang, K. Konishi, M. Nitta, K. Ohashi,
            "Group Theory of Non-Abelian Vortices".
            JHEP 1011:042, (2010). e-Print: arXiv:1009.4794 [hep-th].

            M. Eto, J. Evslin, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci, N. Yokoi (2007),
            "On the moduli space of semilocal strings and lumps",
            Phys. Rev. D76:105002, (2007), arXiv:0704.2218 [hep-th].

            K. Konishi "The Magnetic Monopoles Seventy-Five Years Later",
            Lecture Notes in Physics, (vol. 1, pp. 473-532). (2007). ISBN-10: 3540742328: Springer.

            M. Eto, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci, N. Yokoi,
            "Non-Abelian Vortices of Higher Winding Numbers",
            Phys. Rev. D, vol. D74, 065021, (2006).

            K. Konishi, R. Auzzi, S. Bolognesi, J. Evslin,
            "NonAbelian monopoles and the vortices that confine them",
            Nucl. Phys. B686, 119 (2004).

            K. Konishi, R. Auzzi, S. Bolognesi, A. Yung, J. Evslin,
            "Nonabelian superconductors: vortices and confinement in N=2 SQCD",
            Nucl. Phys. B673, 187 (2003). e-Print: hep-th/0307287.

            G. Carlino, K. Konishi, H. Murayama,
            "Dynamical symmetry breaking in supersymmetric SU(n(c)) and USp(2n(c)) gauge theories",
            Nucl. Phys. B 608, 51 (2001) e-Print: hep-th/0005076.

Tuesday, April 12, 2011
20                                       0

                                                                                                                                                                                                        Figure 3: The four complex profile functions

                                                                                                                                                                                                          20

                                                                                                                                                                                                          10

                                                                                                                                                                                                           0

                          “Fractional vortex”                                                                               Eto et. al. ’09
                                                                                                                                                                                                         !10

                                                                                                                                                                                 l e - Vo rtex
                                                                                                                                                                               o
                                                                                                                                                                         Monop plex
                                                                                                                                                                             com            origon
                                                                                                                                                                                                   i,
                                                                                                                                                                                u d n a son, D ni ’11    !20
                                                                                                                                                                           i, G               eli
                                                                                                                                                                   Ciprian Konishi, Mich                       !30   !20      !10      0        10
                                                                                                                                                                          ri,
                                                                                                                                                                   Fujimo
                           Gauge profile function f ! Ρ,z"                                                                                                                                      Figure 4: The behaviour of the magnetic field in the complex
                                                                                                               Gauge profile function l! Ρ,z"

             !1.0

              !1.5
                                                                                                                                                                               1.0
                                                                                                                                                                                                                            15
                                                                                           20
                                                                                                                                                                              0.5

                  !2.0
                     20                                                              15                 !50
                                                                                                                                                                             0.0
                           10                                                                                                                                           0
                                                                            10
                                                                                                                   0
                                                                                                                                                              10
                                 0
                                                                  5                                                                                 20
                                      !10                                                                              50
                                                                                                                                           30

                                                 !20    0                                                                       40

                           Scalar profile function s! Ρ,z"
                                                                                                                   Quark profile function q! Ρ,z"

Fig. 5: The energy (the left-most and the 2nd left panels) and the magnetic flux (the 2nd right panels) density,
            1.0

                                                                                            20
                                                                                                 1.0

                                                                    Vortex   orientational  zeromodes
             0.5
                                                                                                  0.5
                                                                                                                                                                                   40
                                                                                      10

together with the boundary values (A, B) (the right-most panel) for the
                  0.00

                           5
                                                                        minimal  0lump of the  first type in the
                                                                                                       0.0

                                                                                                              50
                                                                                                                                                                   20
                                                                                                                                                                        30

                                 10
                                                                                                                            0

strong gauge coupling limit. The moduli parameters are fixed as a1 = 0, a2 = 1, b1 = −1 in Eq. (4.18). The red
                                                                      !10
                                                                                                                                                         10
                                            15
                                                                                                                                     !50
                                                            !20
                                                       20                                                                                       0

dots are zeros of A and  Figure 3:the    black
                                   The four          onefunctions
                                            complex profile is the zero of B. ξ = 1. The last figures illustrates the minimum lump
                                                                                       √
defined   at exactly the orbifold point (see Eq. (4.20)) with Avev = 1/ 2, and with b = 0.8.
 Tuesday, April 12, 2011
                                                 20
Dorigoni
           Dorigoniinincollaboration
                        collaborationwith
                                        withVeneziano,
                                             Veneziano,WosiekWosiek
          IDEA:
           IDEA:
            !! Studying
                StudyingQCD-Like
                           QCD-Liketheories
                                       theoriesspectra
                                                spectraininthe theLarge-N
                                                                      Large-Nlimit,
                                                                               limit,
            !! Volume
                Volumeindependence
                         independence++Discretized
                                            DiscretizedLight-Cone
                                                             Light-Conequantization
                                                                           quantization
               ⇒⇒reduces
                    reducescomputation
                             computationtotoquantum
                                               quantummechanics
                                                             mechanicsproblem.
                                                                           problem.
          Model
           ModelStudied:
                   Studied:SYM       reducedtotoNN==(2,
                             SYM4 4reduced               (2,2)2)inindd==22
          Observations:
           Observations:
            !! String-like  spectrumMMn n""TT#∆x$
                String-likespectrum              #∆x$n ,n ,
            !! Quantized
                Quantizeddistance
                            distancebetween     partons#∆x$
                                       betweenpartons        #∆x$n .n .
           |Wavefunctions|2 2inincoordinate
          |Wavefunctions|         coordinatespace
                                              spacefor
                                                    fortwo  twoand
                                                                 andthree
                                                                        threepartons:
                                                                              partons:

                   1.0 1.0                           0.5 0.5                           0.5 0.5
                   0.8 0.8                           0.4 0.4                           0.4 0.4
                   0.6 0.6                           0.3 0.3                           0.3 0.3
                   0.4 0.4                           0.2 0.2                           0.2 0.2
                   0.2 0.2                           0.1 0.1                           0.1 0.1
                   0.0 0.0                           0.0 0.0                           0.0 0.0
                     !100!100!50 !50 0   0 50 50 100 100
                                                       !100!100!50 !50 0   0 50 50 100 100
                                                                                         !100!100!50 !50 0   0 50 50 100 100
                   0.5 0.5                           0.5 0.5                           0.5 0.5
                   0.4 0.4                           0.4 0.4                            0.4 0.4
                   0.3 0.3                           0.3 0.3                            0.3 0.3
                   0.2 0.2                           0.2 0.2                            0.2 0.2
                   0.1 0.1                           0.1 0.1                            0.1 0.1
                   0.0 0.0                           0.0 0.0                           0.0 0.0
                     !100!100!50 !50 0   0 50 50 100 100
                                                       !100!100!50 !50 0   0 50 50 100 100     !50 !50 0     0 50 50 100 100

Tuesday, April 12, 2011
Giampiero Paffuti and Ken Konishi’s hobby:
                                   Quantum Mechanics
           • Generalized uncertainty relations (string theory) ’90
                            ∆x = /∆p + ℷ ∆p    ➯ Minimum physical length in Nature !
           • Cyclic oscillator theorem ’06 :   Microscopic QM systems cannot act as engines

           • New Quantum Mechanics book (800 p. + CD), Oxford Univ. Press (’09)

Tuesday, April 12, 2011
Physics of 2020

                           Be open minded
Tuesday, April 12, 2011
Table: Gauge boson masses
                          Table: Quark masses

 photon ugluons
          (MeV)               Wc±(GeV)
                                  (GeV)               Z (GeV) d (MeV)
                                                   t (GeV)                s (MeV)        b (GeV)
                                                                                                   24.1    Mathematical appendices 761
    0             0          80.425 ± 0.038    91.1876 ± 0.0021
             1.5 − 4          1.15 − 1.35     174.3 ± 5.1         4−8     80 − 130     4.1 − 4.4
                                         Table: Lepton masses
                              Table 24.10
                                                    Table 24.8
                                                                                     Table: Lepton masses
                       νe (eV)
               Table: Neutrino masses νµ (MeV)                              ντ ( MeV)
Remarks
     • We are basically made of

                                  p ∼ uud;           n ∼ udd;       e;        γ
                i.e., of        u, d, e, γ, gluons

    • Nevertheless, baryogenesis (CKM quark mixing, CP violation, B-violation)

                 ➩        all quarks, leptons and gauge bosons of the Table                B.T.W.
                                                                                   fundamental contributions
                                    indispensable                                     by the experimental
                                                                                      HE groups of Pisa
                      for us to be here today                                     • the top quark discovery
                                                                                   • CP in K
                                                                                        • CP in B

Tuesday, April 12, 2011
G.Morchio, F.Strocchi, C.Budroni (dottorando a Siviglia)       Fondamenti della MQ e effetti non perturbativi in teorie di gauge

     1. Algebre di Poisson non commutative, invarianza per diffeomorfismi e quantizzazione

     Risultati: A) MQ sulle varietà differenziabili: Per ogni varietà M esiste unʼunica ∗ algebra A(M), generata dalle
     funzioni f su M e dalle traslazioni infinitesime Tv lungo tutti i campi vettoriali v, con le relazioni di commutazione
      di Lie tra funzioni e campi vettoriali e le relazioni di Lie-Rinehart
       Tf v = 1/2(f Tv + Tv f ) .
     A(M) `e invariante per diffeomorfismi. Le relazioni di Lie-Rinehart sono essenziali per la non proliferazione
      dei gradi di libert`a (associati allʼalgebra di Lie infinito dimensionale dei diffeomorfismi)
     Le rappresentazioni di A(M) sono tutte localmente Schroedinger (in generale con molteplici-
     t`a) e sono classificate dal primo gruppo di omotopia π1(M ), che in generale non `e commutativo
     e d`a perci`o origine a “fasi non abeliane”.

     B) Derivazione della quantizzazione di Dirac senza inconsistenze:

         A ogni varieta `e associata lʼalgebra di Poisson delle funzioni e dei campi vettoriali, con le relazioni di
     Lie-Rinehart, senza altri vincoli su prodotti o commutatori. Tale algebra contiene una variabile centrale
     Z , che commuta e ha Poisson nullo con tutti gli el-
     ementi e che mette in relazione Poisson e commutatori:
     Tv f (x) − f (x)Tv = Z {Tv , f (x)}

     Z = −Z ∗. Nelle rappresentazioni irriducibili

     Soli risultati possibili:

     - c = 0: Meccanica Classica lagrangiana
     - Meccanica quantistica come sopra con c = i

Tuesday, April 12, 2011
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