Non-lattice simulation of supersymmetric gauge theories as a probe to quantum black holes and strings Jun Nishimura (KEK) Plenary talk at LATTICE 2009,

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Presentation transcript:

Non-lattice simulation of supersymmetric gauge theories as a probe to quantum black holes and strings Jun Nishimura (KEK) Plenary talk at LATTICE 2009, Beijing, China, July 30, ’09. 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

0. Introduction

Gauge/gravity duality (a conjecture from superstring theory) Maldacena (’97) 6225 cites on SPIRES U(N) supersymmetric Yang-Mills theory (SYM) with 16 (32) supercharges a classical solution of 10d supergravity (SUGRA) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... Why interesting ? realization of an old idea by ’t Hooft (’73) emergent space-time applications: ultimate goal: strong-weak duality large N gauge theory string theory anti-de Sitter space, black hole geometry at finite T hadron and condensed matter physics, from curved space-time black hole thermodynamics, from gauge theory non-perturbative & background indep. formulation of string theory Studies of strongly coupled gauge theory are important ! 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... Monte Carlo studies supersymmetry translational symmetry broken by the lattice SUSY can be restored in the continuum limit. (Typically, fine-tuning is necessary.) recent developments in “lattice SUSY” lattice actions with various symmetries e.g.) preserving 1 supercharge using topological twist non-lattice simulations of SYM with 16 supercharges 1d gauge theory extension to 3d, 4d gauge theory using the idea of large N reduction Catterall’ talk, Rm.2, 14:30- superconformal (AdS/CFT) 32 c.f.) Kaplan-Unsal (’05), Elliott-Giedt-Moore (’08) Catterall (’08) No fine-tuning ! 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... Plan of the talk 0. Introduction 1. Non-lattice simulation of 1d SYM with 16 supercharges black hole thermodynamics from 1d SYM Schwarzschild radius from Wilson loop 2. Extension to higher dim. (based on large-N reduction) 　　　　　preliminary results for Wilson loop and 2pt correlators 3. Summary 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

1. Non-lattice simulation of 1d SYM with 16 supercharges

Jun Nishimura (KEK) Non-lattice simulation ... 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) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) 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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... Result: 　Polyakov line Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454] High T expansion (including next-leading order) Characteristic behavior of the deconfined phase no phase transition unlike in bosonic case consistent with analyses on the gravity size (Barbon et al., Aharony et al.) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... 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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

More precise comparison Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 [arXiv:0811.3102] corrections slope = 4.6 finite cutoff effects 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... 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) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Prediction from gauge/gravity duality (III) predicted from dual geometry by Sekino-Yoneya (’99) using Gubser-Klebanov-Polyakov-Witten relation (’98) power law behavior reproduced from 1d SYM work in progress Hanada-J.N.-Sekino-Yoneya 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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

Jun Nishimura (KEK) Non-lattice simulation ... 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) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

A novel large N reduction for SYM on (cont’d) Ishiki-Ishii-Shimasaki -Tsuchiya (’08) SYM on 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

circular Wilson loop in conformal mapping grand circle Erickson-Semenoff-Zarembo (’00), Drukker-Gross (’00), Pestun (’07) (agree with the result from dual geometry) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Result: circular Wilson loop (preliminary) 1 2 work in progress Honda-Ishiki-J.N.-Tsuchiya strong coupling weak coupling all order 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... Chiral primary operators e.g.) 2-pt function large-N reduction SUSY non-renormalization theorem 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

Jun Nishimura (KEK) Non-lattice simulation ... 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. 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

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 : 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...

3. Summary

Jun Nishimura (KEK) Non-lattice simulation ... Summary non-lattice simulations of supersymmetric large N gauge theories revealed direct connections to gravity as predicted by gauge/gravity duality models with maximal supersymmetries 16 supercharges (1d SYM) 32 supercharges ( SYM on ) 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) 2009.7.30 LATTICE 2009 Jun Nishimura (KEK) Non-lattice simulation ...