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Numerical tests of the gauge-gravity duality and beyond

Numerical tests of the gauge-gravity duality and beyond. Jun Nishimura (KEK, SOKENDAI). KEK, lattice meeting for future prospects, KEK, Feb. 15, 2010. Ref.) Hanada-J.N.-Takeuchi, PRL 99 (’07) 161602

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Numerical tests of the gauge-gravity duality and beyond

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  1. Numerical tests of the gauge-gravity duality and beyond Jun Nishimura (KEK, SOKENDAI) KEK, lattice meeting for future prospects, KEK, Feb. 15, 2010. Ref.) Hanada-J.N.-Takeuchi, PRL 99 (’07) 161602 Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 Hanada-Miwa-J.N.-Takeuchi, PRL 102 (’09) 181602 Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 Ishiki-Kim-J.N.-Tsuchiya, PRL 102 (’09) 111601 Hanada-J.N.-Sekino-Yoneya, arXiv:0911.1623[hep-th]

  2. 0. Introduction

  3. Increasingly many applications of the gauge/gravity duality strongly coupled gauge theory classical gravity theory quantum • hadron physics confined phase (Sakai-Sugimoto model etc.) mass spectrum, effective coupling, nuclear forces,… deconfined phase (quark-gluon plasma) transport coefficients (viscosity etc.),… • condensed matter physics superfluidity, superconductivity, quantum Hall systems,… Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  4. All this is nice! But, to what extent does the duality really hold quantitatively ? • AdS/CFT 4d SU(N) SYM theory with maximal SUSY (super) Conformal Field Theory • large N lim. • strong coupling lim. string loop corrections can be neglected Classical gravity theory becomes valid. Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  5. Monte Carlo simulation of 1d SYM with 16 supercharges precision test of the gauge/gravity duality from first principles (non-conformal case) • internal energy v.s. temperature microscopic origin of black hole thermodynamics • Wilson loop One can see Schwarzschild radius from gauge theory! • correlation functions confirmation of the GKP-Witten prescription Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  6. Plan of the talk • 0. Introduction • 1. An intuitive argument for the gauge/gravity duality • 2. Monte Carlo simulation of 1d SYM with 16 supercharges • 3. Black hole thermodynamics from 1d SYM • 4. corrections and string loopcorrections • 5. Wilson loop and correlation functions • 6. Extension to higher dimensions based on large-N reduction • 7. Summary Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  7. An intuitive argument for the gauge/gravity duality

  8. Gauge/gravity duality (a conjecture from superstring theory) Maldacena (’97) 6607 cites on SPIRES U(N) supersymmetric Yang-Mills theory (SYM) with 16 (32) supercharges a classical solution of 10d supergravity (SUGRA) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  9. An intuitive argument for the conjecture D brane　　 　“soliton solution” in superstring theory (Dirichlet) emission of a graviton propagation of a gauge particle dim U(N) SYM low energy limit curved 10d space-time N Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  10. 2. Monte Carlo simulation of 1d SYM with 16 supercharges Hanada-J.N.-Takeuchi, PRL 99 (’07) 161602

  11. 1d SYM with 16 supercharges 1d gauge theory p.b.c. anti p.b.c. (without loss of generality) low T strongly coupled dual gravity description high T weakly coupled high T exp. Kawahara-J.N.-Takeuchi (’07) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  12. should be fixed by imposing Non-lattice simulation Hanada-J.N.-Takeuchi, PRL 99 (07) 161602 [arXiv:0706.1647] Note: Gauge symmetry can be fixed non-perturbativelyin 1d. • static diagonal gauge : • residual gauge symmetry : RHMC algorithm can be used efficiently (Fourier acceleration without extra cost etc.) c.f.) lattice approach : Catterall-Wiseman, JHEP 0712:104,2007 Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  13. 3. Black hole thermodynamics from 1d SYM Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601

  14. quantum description of the states inside the BH Prediction from gauge/gravity duality (I) • dual geometry Hawking’s theory black hole thermodynamics 7.41 Klebanov-Tseytlin (’96) Gauge/gravity duality predicts that this should be reproduced by 1d SYM. large-N, low T microscopic origin of the black hole thermodynamics Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  15. Dual gravity description After taking the decoupling limit : range of validity: Black hole thermodynamics Hawking temperature : Bekenstein-Hawking entropy : Klebanov-Tseytlin (’96) 7.41 Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  16. Result: Internal energy Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454] free energy high T expansion (incl. next-leading order) result obtained from 10d BH Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  17. Digression : 8 supercharge case Hanada, Matsuura, J.N., Robles-Llana, in progress • b=2 obtained from Born-Oppenheimer • analysis in gauge theory by A.Smilga (’09) • What is the gravity dual ? Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  18. corrections and string loop corrections Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 Ishiki-Hanada-Hyakutake-J.N., work in progress

  19. corrections to SUGRA action low energy effective action of type IIA superstring theory tree-level scattering amplitudes of the massless modes leading term : type IIA SUGRA action explicit calculations of 2-pt and 3-pt amplitudes 4-pt amplitudes Complete form is yet to be determined, but we can still make a dimensional analysis. Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  20. Black hole thermodynamics with corrections curvature radius of the dual geometry More careful treatment leads to the same conclusion. (Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  21. confronting Monte Carlo data Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 [arXiv:0811.3102] corrections slope = 4.6 finite cutoff effects Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  22. string loop corrections to SUGRA action known from IIA string theory 1-loop Bern, Rozowsky, Yan Bern, Dixon, Dunbar, Perelstein, Rozowsky 2-loop Using Kawai-Lewellen-Tye relation to SYM amp. Only meta-stable vacuum at finite N (flat directions) negative specific heat ! small N, very low T regime Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  23. 1/N corrections (preliminary results) Ishiki-Hanada-Hyakutake-J.N., work in progress Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  24. 5. Wilson loop and correlation functions Hanada-Miwa-J.N.-Takeuchi, PRL 102 (’09) 181602 Hanada-J.N.-Sekino-Yoneya, arXiv:0911.1623[hep-th]

  25. Prediction from gauge/gravity duality (II) SYM probe D-brane Maldacena (’98) Rey-Yee (’98) string Wilson loop minimal surface • Schwarzschild radius from Wilson loop (in 1d SYM) 1.89 Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  26. Result: Wilson loop Hanada-Miwa-J.N.-Takeuchi, PRL 102 (’09) 181602 [arXiv:0811.2081] Schwarzschild radius from the Wilson loop high T exp. (next-leading) subleading term (perturbative corrections) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  27. Prediction from gauge/gravity duality (III) correlation functions in gauge theory generating functional operator-field correspondence gauge gravity Gubser-Klebanov-Polyakov-Witten relation (’98) SUGRA action evaluated at the classical solution with the boundary condition Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  28. Result: 2pt correlation functions e.g.) predicted from dual geometry by Sekino-Yoneya (’99) using Gubser-Klebanov-Polyakov-Witten relation (’98) power law behavior reproduced from 1d SYM Hanada-J.N.-Sekino-Yoneya, arXiv:0911.1623[hep-th] Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  29. 6. Extension to higher dimensionsbased on large-N reduction

  30. Large N reduction Eguchi-Kawai (’81) Bhanot-Heller-Neuberger (’82) Gonzalez-Arroyo & Okawa (’82) U(N) gauge theory in D-dim. torus reduce to a point large-N reduced model c.f.) QCD at Narayanan-Neuberger (’03) Bringoltz-Sharpe (’09) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  31. A novel large N reductionfor SYM on Ishiki-Ishii-Shimasaki -Tsuchiya (’08) reduce to a point 1d SYM + mass deformation (preserving 16 SUSY) many classical vacua preserving 16 SUSY all degenerate Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  32. SYM on A novel large N reductionfor SYM on (cont’d) Ishiki-Ishii-Shimasaki -Tsuchiya (’08) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  33. A check in the weak coupling limit Ishiki-Kim-J.N.-Tsuchicya Phys.Rev.Lett.102 (09) 111601[arXiv:0810.2884] deconfinement transition at finite T known results for SYM on (Aharony et al. ’03) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  34. circular Wilson loop in conformal mapping grand circle Erickson-Semenoff-Zarembo (’00), Drukker-Gross (’00), Pestun (’07) (agree with the result from dual geometry) Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  35. 1 2 Result: circular Wilson loop (preliminary) work in progress Honda-Ishiki-J.N.-Tsuchiya strong coupling weak coupling all order Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  36. e.g.) Chiral primary operators 2-pt function large-N reduction SUSY non-renormalization theorem Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  37. Result : 2pt function of chiral primary operators (preliminary) work in progress Honda-Ishiki-Kim-J.N.-Tsuchiya free theory result for the reduced model for N=14 result for SYM indication of SUSY non-renorm. th. Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  38. More interesting quantities • rectangular Wilson loop, higher point functions in SYM on c.f.) Berenstein-Cotta-Leonardi (’08) calculable by using the large-N reduced model highly non-trivial test of AdS/CFT Due toconformal symmetry i.e., Gauge/gravity duality predicts : Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  39. 7. Summary and future prospects

  40. Summary and future prospects • Monte Carlo simulations of 1d U(N) SYM with 16 supercharges Precision test of the gauge/gravity duality from first principles (non-conformal case) negative specific heat ? Black hole thermodynamics including corrections Schwarzschild radius from Wilson loop GKP-Witten prescription for correlation functions • gauge/gravity duality seems to hold including corrections non-perturbative definition of superstring theory on a particular curved background • 1d U(N) SYM with 8 supercharge E v.s. T relation shows clear power law (p=2); gravity dual ? Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

  41. Summary and future prospects • extension to models in higher dimensoins 1d SYM16 supercharges SYM on 32 supercharges Superconformal ! a novel large-N reduction (preserving 16 SUSY) restoration of 32 SUSY at large N : yet to be seen at strong coupling SYM on , theories with less SUSY (easier) • IKKT matrix model (Ishibashi-Kawai-Kitazawa-Tsuchiya ’96) 0d reduction of the 1d SYM with 16 superchages Emergence of 4d space-time from non-perturbative superstring theory Anagnostopoulos, Aoyama, Azuma, Hanada, J.N. Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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