Chaos n QFT (PRL) w/ K.Murata, K.Yoshida Chaos of chiral condensates in gauge theories

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1 KEK theory workshop, 6 th December, 2016 Chaos n QFT Koji Hashimoto (Osaka u) (PRL) w/ K.Murata, K.Yoshida Chaos of chiral condensates in gauge theories w/ N.Tanahashi Universality in chaos of particle motion near black hole horizon

2 How complex is a given QFT? Complexity QFT 1 QFT 2 QFT 3

3 Chaos hidden in strongly coupled theories Chaos or quarks? ChaoKc condensate in inear sigma model ChaoKc condensate in holographic super QCD Horizon is a nest of chaos 4p p p 3p

4 1-1 Chaos : sensi+ve to ini+al condi+ons Classical chaos = Non-periodic bounded orbits sensikve to inikal condikons in non-linear determiniskc dynamical systems Poincare seckon, scauered Lyapunov exponent, posikve 1 d(t) L = lim lim log t d(0) 0 t d(0) d(0) d(t) d(t) d(0) exp[lt]

5 1-2 Measuring complexity of QFT? SM : Gauge fields, Higgs, MaUer fermions Bosonic. Classical analysis possible - Yang-Mills chaos - Yang-Mills-Higgs chaos QuesKon : Fermion?? -- and Quantum?? [MaKnyan, Savvidy, Savvidy `81] [Savvidy `84] [Muller, Trayanov `92] [Biro, MaKnyan, Muller `94]

6 1-3 Quantum Problem: Lyapunov washed out? Schrodinger equakon is linear, thus no chaos!? Quantum chaos = QuanKzing classically chaokc system Character: Energy level spacing is Wigner, not Poisson Atomic spectra of Lithium under electric field [Courtney, Spellmeyer, Jiao, Kleppner, 95] Spacing of hadron spectra [Pando-Zayas, 00]

7 1-4 Solu+on for a Quantum Lyapunov Our solukon: Employing large N limit General QFT E High energy limit 0 Classical limit N Large N limit Another solukon: Out-of-Time-Ordered correlators 2 Q(t) Q(t)P (0)Q(t)P (0) Q(0) [Larkin, Ovchinnikov `69] [Kitaev `14] [Maldacena, Shenker, Stanford `15]

8 Chaos hidden in strongly coupled theories Chaos or quarks? ChaoKc condensate in inear sigma model ChaoKc condensate in holographic super QCD Horizon is a nest of chaos 4p p p 3p

9 2-1 Effec+ve QCD: linear sigma model The model describes QCD with: - 1-flavor, ignoring anomaly - 2-flavor, neutral pion sector BoUom Breaking of U(1) (or sigma_3 of SU(2)) - spontaneously by chiral condensate - explicitly by quark mass

10 2-2 Chaos of chiral condensate Poincare seckons for E=100[MeV] E=130[MeV] E=140[MeV] E=150[MeV] E=160[MeV] E=200[MeV]

11 2-3 Posi+ve Lyapunov exponent

12 Chaos hidden in strongly coupled theories Chaos or quarks? ChaoKc condensate in inear sigma model ChaoKc condensate in holographic super QCD Horizon is a nest of chaos 4p p p 3p

13 3-1 AdS/CFT gives classical meson theory Classical meson ackon = 2 D7-branes in AdS Mesons Meson masses: [Kruczenski, Mateos, Myers, Winters `03] EffecKve theory of mesons of N=2 supersymmetric QCD - N=4 Super Yang-Mills plus N=2 quark hypermulkplets - Parameter of the theory: - 2-flavor, quark mass - SU( ) gauge group with large - Large t Hooq coupling

14 3-2 Poincare sec+ons of quark condensate Chaos-Order phase transikon: Poincare seckons for E=0.05 E=0.1 E=0.3 E=0.6 E=0.8 E=1 Ref. [MaKnyan, Savvidy, Savvidy, `81]

15 3-3 Lyapunov exponent of quark condensate Lyapunov exponent

16 Chaos hidden in strongly coupled theories Chaos or quarks? ChaoKc condensate in inear sigma model ChaoKc condensate in holographic super QCD Horizon is a nest of chaos 4p p p 3p

17 4- SYK model : dual to black hole? Lyapunov upper bound (conjecture) for thermal OTO L 2 T SYK (Sachdev-Ye-Kitaev) model H = 1 4! N i,j,k,l=1 j [ijkl] i j k l Solvable at Large N and strong coupling Shown to saturate the bound [Maldacena, Shenker, Stanford `15] Suggested from AdS/CFT with black holes [Kitaev `15][Sachdev,Ye `95] (1+0 dim., N Majorana fermions, disordered interackon) N j,k,l=1 j ijkl j ijkl =6J 2 J [Kitaev `15] [Maldacena, Stanford `16] See for modified models [Gross, Rosenhaus `16] [WiUen `16]

18 4-2 Black hole is a nest of chaos Shock wave delay horizon [Shenker, Stanford `13,`14] Universal chaos in parkcle mokon near BH [Tanahashi, KH 16] Pot. E t 2 t 1 separatrix Black hole is a fast scrambler? [Sekino, Susskind `08] 2d dilaton gravity dual to SYK [Almheiri, Polchinski `14] [Engelsoy, Martens, Verlinde `16] E t 2 = 8 TM e2 T (t 2 t 1 ) r 0 r C ṙ (2 T ) 2 (r r 0) 2

19 4-3 Red ship giving a chaos Simple model: harmonic oscillator near horizon [Tanahashi, KH `16] L = f(x) ``horizon f(x) ẋ 2 f(x) 4 Tx ẏ (x x c ) 2 + y 2 Low energy High energy

20 4-3 Red ship giving a chaos Simple model: harmonic oscillator near horizon [Tanahashi, KH `16] L = f(x) ``horizon f(x) ẋ 2 f(x) 4 Tx ẏ (x x c ) 2 + y 2 Low energy High energy

21 Chaos hidden in strongly coupled theories Chaos or quarks? ChaoKc condensate in inear sigma model ChaoKc condensate in holographic super QCD Horizon is a nest of chaos 4p p p 3p

22 1) Holography? Discussion: chao+c QFT Integrability versus chaos. Black holes? InformaKon loss? Upper bound of yapunov? 2) Entropy produckon? Phase transikon? [Aref eva, Medvedev, Rytchkov, Volovich 99] [Asano, Kawai, Yoshida 15] [Hawking 14] [Farahi, PandoZayas 14] [Maldacena, Shenker, Stanford 15] Kolmogorov-Sinai entropy = Shannon entropy rate [Latora, Branger, 99] ThermalizaKon from color glass? [Kunihiro, Muller, Ohnishi, Schafer, 10] 3) Cosmology? Separatrix. Hybrid inflakon [Linde 93] Brane inflakon [Dvali, Tye 99] Racetrack inflakon [Blanco-Pillado et al. 04]