Gauge/gravity duality

・ Strongly coupled gauge theory ( in large N limit )

・ String theory

gravity in a curved space

AdS/CFT [1997, Maldacena]D-brane

graviton：　 closed string

：　 open string gauge field

Applications of gauge/gravity duality

1. Non-perturbative formulation of string theory?

2. Quantum behavior of black holes

“ resolving black hole information loss problem”

3. Holographic QCD, Holographic superconductor, …

“ understanding of strongly coupled theories from gravity side”

The duality is not a theorem, but a conjecture.

Verification is important.

New frontier in lattice gauge theories

　 　 　 　 　

Gauge/gravity duality

[1997, Maldacena,…]

New studies which bridge the gap between gauge theories and the theories of gravity.

Lattice supersymmetry

[2004, Kaplan, Sugino,…]

Gauge/gravity duality － From lattice gauge theory to Black hole

Sakata Memorial KMI Workshop on SCGT15

＠ Sakata-Hirata Hall, Nagoya Univ., March 5, 2015

Daisuke Kadoh (KEK)

D.K. and S.Kamata, PoS LATTICE 2012:064, PoS(LATTICE 2013) 343D.K. and S.Kamata, in preparation

Talk plan

１ . Motivation

２ . １ -dim SYM and gauge/gravity duality

３ . 1-dim SYM on the lattice

- Lattice action

- SUSY Ward-Takahashi identity

４． Our lattice result of internal energy of black hole

５． Summary

２．１ -dim SYM with 16 supercharges

and gauge/gravity duality

Continuum action

Sixteen SUSY-invariance

　

1-dim SYM with 16 supercharges

: sixteen Grassmann parameters

: scalar fields

: gauge field

: fermi fields

1D SYM with 16 supercharges

Thermodynamics of black hole

Gauge/gravity duality in 1-dim SYM

N D0-branes solution in IIA superstring

t

N D0-branes

black hole

1996 Klebanov -Tseytlin

BH internal energy in gravity side

large

We compute physical quantities of black hole from lattice simulations of gauge theory side to test the duality.

Previous numerical results (1) Non-latticeM.Hanada, J. Nishimura et al. (2007-2009)

temperature

Good agreement

with gravity side

Black hole internal energy

Regularized by momentum sharp cutoff

Previous numerical results (2) Lattice

S. Catterall and T. Wiseman (2007-2010)

Compact link field (exact gauge invariance)SUSYs are broken by lattice cut-off

Disagreement …?

Lattice is inferior to the simple momentum sharp cutoff ?

Symmetries at regularized level

2-chargesSUSY

gauge sym.(BRST sym.)

Non-lattice(Nishimura et al)

Lattice(Catterall et al)

None OK OK

Lattice(this research)

We employ a lattice action with two exact supercharges,proposed by F.Sugino [Sugino, 2005].

None None

２． 1-dim SYM on the lattice

Q-exact action

Lattice action

Lattice action

up to gauge transformation

Two exact supercharges

[2005, F.Sugino]

discretization

two supercharges

SUSY WTI

Numerical results of SUSY Ward-Takahashi identity

SUSY WTI holds. All sixteen supercharges are recovered for a<<1.

４． Internal energy of black hole

Lattice result of internal energy of black hole

Kawahara-Takeuchi-Nishimura(2007),D.K. and Kamata (in preparation)

HTE (NLO,N=14)

prediction in gravity side

(1996 Klebanov -Tseytlin)

Low temperature

- Fit formula at NLO

[Nishimura’s non-lattice result(2009)]

[gravity side]

[our result]

Polyakov loop, SU(3)

Reconsideration of Catterall-Wiseman’s results

“High temperature” “Low temperature”

Catterall-Wiseman This study

５． Summary

Summary

1d SYM with 16 supercharges

N D0-branes in type IIA superstring

Sugino’s lattice action with two exact supercharges.

Numerical results of SUSY WTI suggested us that the lattice action reproduces correct continuum theory.

Internal energy of black hole

Future directions

Simulation of 1d SYM with 16 supercharges

Continuum limit of NLO coefficient Explanation of leading order coefficient, 7.41 Other physical quantities(Wilson loop,…) 1/N corrections

Verification of gauge/gravity duality in higher dimensions

2-dim SYM <=> N D1-branes in type IIB superstring

Lattice simulations, D.K. and Eric Giguere

NLO

Nishimura’s non-lattice result(2009) :

Our result :