Numerical tests of the gauge-gravity duality and beyond

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Presentation transcript:

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]

0. Introduction

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,… 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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. 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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 loop corrections 5. Wilson loop and correlation functions 6. Extension to higher dimensions based on large-N reduction 7. Summary 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

An intuitive argument for the gauge/gravity duality

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) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... Non-lattice simulation Hanada-J.N.-Takeuchi, PRL 99 (07) 161602 [arXiv:0706.1647] Note: Gauge symmetry can be fixed non-perturbatively in 1d. static diagonal gauge : residual gauge symmetry : should be fixed by imposing RHMC algorithm can be used efficiently (Fourier acceleration without extra cost etc.) c.f.) lattice approach : Catterall-Wiseman, JHEP 0712:104,2007 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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 quantum description of the states inside the BH 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... Dual gravity description After taking the decoupling limit : range of validity: Black hole thermodynamics Hawking temperature : Bekenstein-Hawking entropy : 7.41 Klebanov-Tseytlin (’96) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 ? 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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

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. 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

confronting Monte Carlo data Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 [arXiv:0811.3102] corrections slope = 4.6 finite cutoff effects 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

1/N corrections (preliminary results) Ishiki-Hanada-Hyakutake-J.N., work in progress 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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]

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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] 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

6. Extension to higher dimensions based on large-N reduction

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

A novel large N reduction for 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 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

A novel large N reduction for SYM on (cont’d) Ishiki-Ishii-Shimasaki -Tsuchiya (’08) SYM on 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

circular Wilson loop in conformal mapping grand circle Erickson-Semenoff-Zarembo (’00), Drukker-Gross (’00), Pestun (’07) (agree with the result from dual geometry) 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Result: circular Wilson loop (preliminary) 1 2 work in progress Honda-Ishiki-J.N.-Tsuchiya strong coupling weak coupling all order 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... Chiral primary operators e.g.) 2-pt function large-N reduction SUSY non-renormalization theorem 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality... 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. 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

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 to conformal symmetry i.e., Gauge/gravity duality predicts : 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

7. Summary and future prospects

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 ? 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...

Summary and future prospects extension to models in higher dimensoins 1d SYM 16 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. 2010.2.15 Lattice meeting Jun Nishimura (KEK) Numerical tests of the gauge-gravity duality...