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Chaos of chiral condensate
QFT workshop, YITP, 10 August, 2016
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Chaos of chiral condensate Koji Hashimoto (Osaka u) w/ Keiju Murata - - PowerPoint PPT Presentation
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 :
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Chaos hidden in strongly coupled theories
Discussion: chaoLc QFT ChaoLc condensate in Linear sigma model ChaoLc condensate in holographic Super QCD Chaos : sensiLve to iniLal condiLons 1 2 3 4
1p 3p 3p 1p
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Chaos : sensi-ve to ini-al condi-ons
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Classical chaos = Non-periodic bounded orbits sensiLve to iniLal condiLons in non-linear determinisLc dynamical systems
L = lim
t→∞ lim d(0)→0
1 t log d(t) d(0)
d(t) ∼ d(0) exp[Lt] d(t)
d(0)
Lyapunov exponent, posiLve Poincare secLon, scaXered
1
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Chaos hidden in strongly coupled theories
Discussion: chaoLc QFT ChaoLc condensate in Linear sigma model ChaoLc condensate in holographic Super QCD Chaos : sensiLve to iniLal condiLons 1 2 3 4
1p 3p 3p 1p
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Effec-ve QCD: linear sigma model
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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
- explicitly by quark mass
2-1
BoXom
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Chaos of chiral condensate
E=100[MeV] E=130[MeV] E=140[MeV] E=150[MeV] E=160[MeV] E=200[MeV] Poincare secLons for
2-2
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8
5 10 15 20 25 30 35 40 130 140 150 160 170 180
Posi-ve Lyapunov exponent
2-3
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Chaos hidden in strongly coupled theories
Discussion: chaoLc QFT ChaoLc condensate in Linear sigma model ChaoLc condensate in holographic Super QCD Chaos : sensiLve to iniLal condiLons 1 2 3 4
1p 3p 3p 1p
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Exact classical meson theory of SQCD
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
3-1
Meson masses: [Kruczenski, Mateos, Myers, Winters 03]
Classical acLon
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Chaos of quark condensate
E=0.05 E=0.1 E=0.3 E=0.6 E=0.8 E=1 Chaos-Order phase transiLon:
3-2
Poincare secLons for
- Ref. [MaLnyan, Savvidi, Savvidi, 81]
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Smaller Nc, more chao-c
3-3
Lyapunov exponent
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Chaos hidden in strongly coupled theories
Discussion: chaoLc QFT ChaoLc condensate in Linear sigma model ChaoLc condensate in holographic Super QCD Chaos : sensiLve to iniLal condiLons 1 2 3 4
1p 3p 3p 1p
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Discussion: chao-c QFT
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2) Entropy producLon? Phase transiLon is a thermal entropy producLon. Kolmogorov-Sinai entropy = Shannon entropy rate [Latora, Branger,
99]
1) Holographic principle? Integrability versus chaos. Black holes? InformaLon loss? Upper bound of chaos?
[Hawking 14] [Farahi, PandoZayas 14] [Aref’eva, Medvedev, Rytchkov, Volovich 99] [Asano, Kawai, Yoshida 15]
3) Standard Model? Cosmology? Higgs criLcality? Higgs inflaLon? Anarchy? ThermalizaLon from color glass?
[Kunihiro, Muller, Ohnishi, Schafer, 10] [Maldacena, Shenker, Stanford 15]
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Chaos hidden in strongly coupled theories
Discussion: chaoLc QFT ChaoLc condensate in Linear sigma model ChaoLc condensate in holographic Super QCD Chaos : sensiLve to iniLal condiLons 1 2 3 4
1p 3p 3p 1p
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Deriva-on via AdS/CFT
NC D3-brane 2 D7-branes N=4 SU(Nc) Super Yang-Mills + N=2 quark hypermultiplet D7-branes in AdS5×S5 meson
[Karch, Katz 02]
FluctuaLon acLon of 2 D7-branes in AdS5 x S5
A1
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