Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N

TL;DR

This paper tests the gauge/gravity duality conjecture for D0-branes at finite temperature and N using Monte Carlo simulations of the BFSS matrix model, confirming predictions from superstring theory.

Contribution

It provides the first direct numerical evidence supporting the duality at finite N and temperature, including string loop and ' corrections.

Findings

Results match gravity predictions with ' corrections at large N.

Results agree with string loop corrections at small N.

Supports the validity of the duality at finite N.

Abstract

According to the gauge/gravity duality conjecture, the thermodynamics of gauge theory describing D-branes corresponds to that of black branes in superstring theory. We test this conjecture directly in the case of D0-branes by applying Monte Carlo methods to the corresponding gauge theory, which takes the form of the BFSS matrix quantum mechanics. In particular, we take the continuum limit by extrapolating the UV cutoff to infinity. First we perform simulations at large N so that string loop corrections can be neglected on the gravity side. Our results for the internal energy exhibit the temperature dependence consistent with the prediction including the \alpha ' corrections. Next we perform simulations at small N but at lower temperature so that the \alpha ' corrections can be neglected on the gravity side. Our results are consistent with the prediction including the leading string loop correction, which suggests that the conjecture holds even at finite N.