Precision lattice test of the gauge/gravity duality at large-$N$

TL;DR

This paper performs large-scale lattice simulations of D0-brane quantum mechanics at various temperatures to test the gauge/gravity duality, successfully confirming supergravity predictions for black hole internal energy from the gauge theory.

Contribution

First large-scale lattice simulation of D0-brane quantum mechanics confirming supergravity predictions at finite temperature.

Findings

Confirmed supergravity prediction for black hole internal energy.

Constrained stringy corrections to the internal energy.

Achieved large-$N$ and continuum limits at multiple temperatures.

Abstract

We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-$N$ and continuum limits of the gauge theory are taken for the first time at various temperatures $0.4 \leq T \leq 1.0$. As a way to directly test the gauge/gravity duality conjecture we compute the internal energy of the black hole directly from the gauge theory and reproduce the coefficient of the supergravity result $E/N^2=7.41T^{14/5}$. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.