Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges

TL;DR

This paper uses lattice simulations to explore the gauge/gravity duality in one-dimensional supersymmetric Yang-Mills theory, confirming the duality's predictions about black hole thermodynamics at low temperatures.

Contribution

It provides a detailed implementation of the Sugino lattice action and verifies supersymmetry restoration, supporting the gauge/gravity duality in a non-perturbative setting.

Findings

Lattice results match gravity predictions for internal energy at low temperatures.

Supersymmetry is restored in the continuum limit as shown by Ward-Takahashi identities.

Internal energy approaches black hole thermodynamics predictions for N=14,32.

Abstract

We study the gauge/gravity duality for supersymmetric SU(N) Yang-Mills theory in 1+0 dimension with sixteen supercharges using lattice simulations. The conjectured duality states that the gravity side is described by N D0-branes in type IIA superstring at large N, and the thermal gauge theory reproduces the black hole thermodynamics at low temperature. In this paper, we explain the Sugino lattice action used in the simulations in detail, and examine the supersymmetric Ward-Takahashi identity to confirm the restoration of supersymmetry in the continuum limit. We also estimate the internal energy of the black hole from the lattice results for N=14,32, and find that it smoothly approaches the prediction of the gravity side as the temperature decreases.