Precision test of the gauge/gravity duality in two-dimensional N=(8,8) SYM

TL;DR

This study tests the gauge/gravity duality in two-dimensional N=(8,8) SYM by comparing lattice simulation results of internal energy and pressure with gravitational predictions, confirming the duality's validity at low temperatures.

Contribution

First lattice simulation of 2D N=(8,8) SYM testing gauge/gravity duality through thermodynamic quantities, employing the Sugino action with preserved supersymmetry.

Findings

Lattice results match gravitational predictions for low T_eff.

Duality holds for N=12 at T_eff<0.4.

Internal energy and pressure agree with black 1-brane thermodynamics.

Abstract

The $\epsilon - p$ is calculated from lattice simulations of two dimensional ${\cal N}=(8,8)$ $SU(N)$ SYM to test the gauge gravity duality. We employ the Sugino action with keeping two of sixteen supercharges exactly on the lattice. The thermodynamics of this gauge theory is described by the black 1-branes at low temperature. The internal energy density $\epsilon$ and the pressure $p$ can be analytically estimated in the gravitational theory. The lattice results in $N=12$ show that $\epsilon - p$ of the thermal SYM reproduces the prediction of the gravitational theory for the dimensionless temperature $T_{\rm eff}<0.4$. This clearly indicates that the duality is valid in this system.