View
217
Download
1
Category
Tags:
Preview:
Citation preview
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 :
Recommended