Plenary talk at LATTICE 2009, Beijing, China, July 30, ’09.

Non-lattice simulation of supersymmetric gauge theories as a probe to quantum black holes and strings

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

Jun Nishimura (KEK)

0. Introduction

2009.7.30 LATTICE 2009

Jun Nishimura (KEK) Non-lattice simulation ...

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Gauge/gravity duality (a conjecture from superstring theory)

Maldacena (’97)

U(N) supersymmetric Yang-Mills theory (SYM)with 16 (32) supercharges

a classical solution of 10d supergravity (SUGRA)

6225 cites on SPIRES

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N

Argument for the conjectureD brane 　　　“ soliton solution”

propagation of a gauge particle

(Dirichlet)

emission of a graviton

curved 10d space-timedim U(N) SYM low energy limit

in superstring theory

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Why interesting ? realization of an old idea by ’t Hooft (’73)

emergent space-time

applications:

ultimate goal:

strong-weak duality

anti-de Sitter space, black hole geometry at finite T

Studies of strongly coupled gauge theory are important !

hadron and condensed matter physics, from curved space-timeblack hole thermodynamics, from gauge theory

non-perturbative & background indep. formulation of string theory

large N gauge theory string theory

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Monte Carlo studies

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

supersymmetrytranslational symmetrybroken by the lattice

SUSY can be restored in the continuum limit. (Typically, fine-tuning is necessary.)

No fine-tuning !

recent developments in “lattice SUSY”

c.f.) Kaplan-Unsal (’05), Elliott-Giedt-Moore (’08) Catterall (’08)

Catterall’ talk, Rm.2, 14:30-

superconformal (AdS/CFT)

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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

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

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low T strongly coupledhigh T weakly coupled high T exp.

dual gravity description

1d gauge theory

p.b.c.

anti p.b.c.

(without loss of generality)

1d SYM with 16 supercharges

Kawahara-J.N.-Takeuchi (’07)

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Hanada-J.N.-Takeuchi, PRL 99 (07) 161602 [arXiv:0706.1647]Non-lattice simulation

residual gauge symmetry :

should be fixed by imposing

static diagonal gauge :

Note: Gauge symmetry can be fixed non-perturbatively in 1d.

c.f.) lattice approach : Catterall-Wiseman, JHEP 0712:104,2007

RHMC algorithm can be used efficiently (Fourier acceleration without extra cost etc.)

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Result: 　 Polyakov line

Characteristic behavior ofthe deconfined phase

High T expansion(including next-leading order)

no phase transition unlike in bosonic caseconsistent with analyses on the gravity size (Barbon et al., Aharony et al.)

Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454]

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Prediction from gauge/gravity duality (I) dual geometry

7.41

Gauge/gravity duality predicts that this should be reproduced by 1d SYM. large-N, low T

microscopic origin of the black hole thermodynamics

Hawking’s theory

black hole thermodynamics

quantum description of the states inside the BH

Klebanov-Tseytlin (’96)

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Result: Internal energy

high T expansion(incl. next-leading order)

free energy

result obtained from 10d BH

Anagnostopoulos-Hanada- J.N.-Takeuchi, PRL 100 (’08) 021601 [arXiv:0707.4454]

2009.7.30 LATTICE 2009


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More precise comparison

finite cutoff effects

slope = 4.6

corrections

Hanada-Hyakutake-J.N.-Takeuchi, PRL 102 (’09) 191602 [arXiv:0811.3102]

2009.7.30 LATTICE 2009


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Prediction from gauge/gravity duality (II)

Schwarzschild radius from Wilson loop (in 1d SYM)

1.89

SYM

string

Maldacena (’98)Rey-Yee (’98)

Wilson loop minimal surface

probe D-brane

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Result: Wilson loop

high T exp.(next-leading)

Schwarzschild radiusfrom the Wilson loop

subleading term (perturbative corrections)

Hanada-Miwa-J.N.-Takeuchi, PRL 102 (’09) 181602 [arXiv:0811.2081]

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predicted from dual geometry by Sekino-Yoneya (’99)using Gubser-Klebanov-Polyakov-Witten relation (’98)

e.g.)

work in progressHanada-J.N.-Sekino-Yoneya

power law behaviorreproduced from 1d SYM

Prediction from gauge/gravity duality (III)

2. Extension to higher dimensionsbased on large-N reduction

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Large N reduction

U(N) gauge theory in D-dim. torus

large-N reduced model

reduce to a point

Eguchi-Kawai (’81)Bhanot-Heller-Neuberger (’82)Gonzalez-Arroyo & Okawa (’82)

c.f.) QCD at Narayanan-Neuberger (’03) Bringoltz-Sharpe (’09)

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A novel large N reductionfor SYM on

1d SYM + mass deformation

reduce to a point

(preserving 16 SUSY)

many classical vacua preserving 16 SUSY

all degenerate

Ishiki-Ishii-Shimasaki-Tsuchiya (’08)

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A novel large N reductionfor SYM on (cont’d)

SYM on

Ishiki-Ishii-Shimasaki-Tsuchiya (’08)

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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 resultsfor SYMon

(Aharony et al. ’03)

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circular Wilson loop in

Erickson-Semenoff-Zarembo (’00),Drukker-Gross (’00),Pestun (’07)

(agree with the result from dual geometry)

conformalmapping

grand circle

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Result: circular Wilson loop

all order

weak coupling

strong coupling

work in progressHonda-Ishiki-J.N.-Tsuchiya

1

2

(preliminary)

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Chiral primary operators

large-N reduction

2-pt function

e.g.)

SUSY non-renormalization theorem

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Result : 2pt function of chiral primary operators

free theory result for the reduced model for N=14

result for SYM

indication of SUSY non-renorm. th.

(preliminary)work in progressHonda-Ishiki-Kim-J.N.-Tsuchiya

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More interesting quantities rectangular Wilson loop, higher point functions

in SYM on

highly non-trivial test of AdS/CFT

Due to conformal symmetry

i.e.,

Gauge/gravity duality predicts :

c.f.) Berenstein-Cotta-Leonardi (’08)

calculable by using the large-N reduced model

3. Summary

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models with maximal supersymmetries

16 supercharges (1d SYM)

32 supercharges

Summary non-lattice simulations of supersymmetric large N gauge theories

revealed direct connections to gravity as predicted by gauge/gravity duality

( SYM on )

a novel large-N reduction(preserving 16 SUSY)

restoration of 32 SUSY at large N : yet to be seen at strong coupling

superconformal

SYM on , theories with less SUSY (easier)

Plenary talk at LATTICE 2009, Beijing, China, July 30, ’09.

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Transcript of Plenary talk at LATTICE 2009, Beijing, China, July 30, ’09.