Chaos and Quantum Field Theory 1605.08124 (hep-th) Koji Hashimoto - - PowerPoint PPT Presentation

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Oct 10, 2022 101 likes •350 views

OIST-RIKEN-Osaka joint workshop Big Waves of TheoreFcal Science in Okinawa, at OIST, 7th July, 2016 Chaos and Quantum Field Theory 1605.08124 (hep-th) Koji Hashimoto (Osaka u) w/ Keiju Murata (Keio u) Kentaroh Yoshida (Kyoto u)

SLIDE 1

Chaos and Quantum Field Theory

OIST-RIKEN-Osaka joint workshop “Big Waves of TheoreFcal Science in Okinawa”, at OIST, 7th July, 2016

Koji Hashimoto (Osaka u) w/ Keiju Murata (Keio u) Kentaroh Yoshida (Kyoto u)

1605.08124 (hep-th)

"wPendulum" made by Takashi Yamaguchi

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How is this quantum field theory chosen to be our universe?

19 real parameters
Symmetry group : SU(3) x SU(2) x U(1)
Ma_er content :

quark, lepton, Higgs, gauge bosons

Comlexity (Choas)? How?

SLIDE 3

Which “QCD” is more chao1c?

LQCD = −1

4F a

µνF aµν + ¯

ψi (iγµDµ − mi) ψi

SLIDE 4

Which one is more chao1c?

SLIDE 5

Which one is more chao1c?

SLIDE 6

Chaos hidden in strongly coupled theories

Discussion: chaoFc QFT Chaos in effecFve model of QCD Chaos in exact (supersymmetric) QCD Chaos : sensiFve to iniFal condiFons 1 2 3 4

4p 4p 5p 1p

SLIDE 7

Chaos : sensi1ve to ini1al condi1ons

Classical chaos = Non-periodic bounded orbits sensiFve to iniFal condiFons in non-linear determinisFc dynamical systems Long history

Three-body planetary system [Poincare, 1892]
Atmospheric model, bu_erfly effect [Lorenz, 1963]
Billiard ball [Bunimovich, 1974]
Yang-Mills? [Savvidy 1981, Muller et al. 1992]

Lots of applicaFons InformaFon theory : Kolmogorov-Sinai entropy ThermalizaFon of heavy ion collisions [Kunihiro et al., 2009] Math modeling in chemical reacFons, biology, economy, sociology, traffic forecast, financial crisis, cryptography, etc

1-1

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Poincare sec1on captures chao1c phase

Poincare secFon MoFon in the phase space

1-2

Small energy Large energy

x(t)

˙ x(t)

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Lyapunov exponent is the chaos index

1-3

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

L 0.38 (l1/l2 = 1)

L 0.30 (l1/l2 = 2)

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Chaos in quantum systems?

1-4

Quantum chaos = QuanFzing classically chaoFc system

Atomic energy spectra of Lithium under a constant electric field

Energy level spacings: Wigner, not Poisson

[Pando-Zayas, 00]

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Chaos hidden in strongly coupled theories

Discussion: chaoFc QFT Chaos in effecFve model of QCD Chaos in exact (supersymmetric) QCD Chaos : sensiFve to iniFal condiFons 1 2 3 4

4p 4p 5p 1p

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QCD is truly quantum

2-1

Quarks are confined to form mesons

¯ ψψ ∼ σ ¯ ψγ5ψ ∼ π

Quarks are condensed, to break chiral symmetry spontaneously

¯ ψ ψ

¯ ψ(x) → ¯ ψ(x) exp[iγ5θ]

ψ(x) → exp[iγ5θ]ψ(x)

¯ ψ(x)ψ(x) = 0

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Effec1ve model of QCD: 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
explicitly by quark mass

2-2

Bo_om

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Chaos of quark condensate

E=100[MeV] E=130[MeV] E=140[MeV] E=150[MeV] E=160[MeV] E=200[MeV] Poincare secFons for

2-3

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5 10 15 20 25 30 35 40 130 140 150 160 170 180

Posi1ve Lyapunov exponent

2-4

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Chaos hidden in strongly coupled theories

Discussion: chaoFc QFT Chaos in effecFve model of QCD Chaos in exact (supersymmetric) QCD Chaos : sensiFve to iniFal condiFons 1 2 3 4

4p 4p 5p 1p

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Exact classical meson theory of SQCD

EffecFve theory of mesons of “N=2 supersymmetric QCD”

N=4 Super Yang-Mills plus N=2 quark hypermulFplets
Parameter of the theory:
2-flavor, quark mass
SU( ) gauge group with large
Large ‘t Hoos coupling

3-1

Meson masses: [Kruczenski, Mateos, Myers, Winters 03]

Classical acFon

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Deriva1on via string theory

NC D3-brane 2 D7-branes N=4 SU(Nc) Super Yang-Mills + N=2 quark hypermultiplet D7-branes in AdS5×S5 meson

[Maldacena, 98][Karch, Katz 02]

3-2

=

QCD, purely quantum (strong coupling limit) Classical gravity

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Equivalence to “Yang-Mills-Higgs”

3-3

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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 transiFon:

3-4

Poincare secFons for

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Smaller Nc, more chao1c

Scale invariance

3-5

Lyapunov exponent

SLIDE 22

Chaos hidden in strongly coupled theories

Discussion: chaoFc QFT Chaos in effecFve model of QCD Chaos in exact (supersymmetric) QCD Chaos : sensiFve to iniFal condiFons 1 2 3 4

4p 4p 5p 1p

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Discussion: chao1c QFT

4

2) Entropy producFon? Phase transiFon is a thermal entropy producFon. Kolmogorov-Sinai entropy = Shannon entropy rate [Latora, Branger,

99]

1) Holographic principle? Integrability versus chaos. Black holes? InformaFon 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 criFcality? Higgs inflaFon? Anarchy? ThermalizaFon from color glass?

[Kunihiro, Muller, Ohnishi, Schafer, 10] [Maldacena, Stanford, Susskind, 15]

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