Chaos of chiral condensate Koji Hashimoto (Osaka u) w/ Keiju Murata - PowerPoint PPT Presentation

Q FT w orkshop, YITP, 10 August, 2016 1605.08124 (hep-th) Chaos of chiral condensate Koji Hashimoto (Osaka u) w/ Keiju Murata (Keio u) Kentaroh Yoshida (Kyoto u)

Which one is more chao-c? 2

Chaos hidden in strongly coupled theories Chaos : sensiLve to iniLal condiLons 1 1p ChaoLc condensate in Linear sigma model 2 3 p ChaoLc condensate in holographic Super QCD 3 3 p 4 Discussion: chaoLc QFT 1p

1 Chaos : sensi-ve to ini-al condi-ons Classical chaos = Non-periodic bounded orbits sensiLve to iniLal condiLons in non-linear determinisLc dynamical systems Poincare secLon, scaXered Lyapunov exponent, posiLve 1 t log d ( t ) L = lim t →∞ lim d (0) d (0) → 0 d ( t ) d (0) d ( t ) ∼ d (0) exp[ Lt ] 4

Chaos hidden in strongly coupled theories Chaos : sensiLve to iniLal condiLons 1 1p ChaoLc condensate in Linear sigma model 2 3 p ChaoLc condensate in holographic Super QCD 3 3 p 4 Discussion: chaoLc QFT 1p

2-1 Effec-ve QCD: linear sigma model The model describes QCD with: - 1-flavor, ignoring anomaly - 2-flavor, neutral pion sector Breaking of U(1) (or sigma_3 of SU(2)) - spontaneously by chiral condensate BoXom - explicitly by quark mass 6

2-2 Chaos of chiral condensate Poincare secLons for E=100[MeV] E=130[MeV] E=140[MeV] E=150[MeV] E=160[MeV] E=200[MeV] 7

2-3 Posi-ve Lyapunov exponent 40 35 30 25 20 15 10 5 0 130 140 150 160 170 180 8

Chaos hidden in strongly coupled theories Chaos : sensiLve to iniLal condiLons 1 1p ChaoLc condensate in Linear sigma model 2 3 p ChaoLc condensate in holographic Super QCD 3 3 p 4 Discussion: chaoLc QFT 1p

3-1 Exact classical meson theory of SQCD Classical acLon Meson masses: [Kruczenski, Mateos, Myers, Winters 03] EffecLve theory of mesons of “N=2 supersymmetric QCD” - N=4 Super Yang-Mills plus N=2 quark hypermulLplets - Parameter of the theory: - 2-flavor, quark mass - SU( ) gauge group with large - Large ‘t Hoog coupling 10

3-2 Chaos of quark condensate Chaos-Order phase transiLon: Poincare secLons for E=0.05 E=0.1 E=0.3 E=0.6 E=0.8 E=1 Ref. [MaLnyan, Savvidi, Savvidi, 81] 11

3-3 Smaller Nc, more chao-c Lyapunov exponent 12

Chaos hidden in strongly coupled theories Chaos : sensiLve to iniLal condiLons 1 1p ChaoLc condensate in Linear sigma model 2 3p ChaoLc condensate in holographic Super QCD 3 3 p 4 Discussion: chaoLc QFT 1p

4 Discussion: chao-c QFT 1) Holographic principle? [Aref’eva, Medvedev, Rytchkov, Volovich 99] Integrability versus chaos. [Asano, Kawai, Yoshida 15] Black holes? InformaLon loss? [Hawking 14] [Farahi, PandoZayas 14] Upper bound of chaos? [Maldacena, Shenker, Stanford 15] 2) Entropy producLon? Phase transiLon is a thermal entropy producLon. Kolmogorov-Sinai entropy = Shannon entropy rate [Latora, Branger, 99] ThermalizaLon from color glass? [Kunihiro, Muller, Ohnishi, Schafer, 10] 3) Standard Model? Cosmology? Higgs criLcality? Higgs inflaLon? Anarchy? 14

Chaos hidden in strongly coupled theories Chaos : sensiLve to iniLal condiLons 1 1p ChaoLc condensate in Linear sigma model 2 3 p ChaoLc condensate in holographic Super QCD 3 3 p 4 Discussion: chaoLc QFT 1p

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A1 Deriva-on via AdS/CFT FluctuaLon acLon of 2 D7-branes in AdS 5 x S 5 2 D7-branes meson N C D3-brane N=4 SU(N c ) Super Yang-Mills D7-branes in AdS 5 × S 5 + N=2 quark hypermultiplet [Karch, Katz 02] 17

A 2 Meson, equivalent to old story 18