Extracting black hole physics from the lattice

TL;DR

This paper uses lattice simulations of N D0-branes to explore their dual black hole thermodynamics, addressing divergence issues with a scalar mass regulator and analyzing the phase's impact on simulations.

Contribution

It introduces a scalar mass regulator to handle divergences in lattice simulations of D0-brane quantum mechanics and investigates the phase's role in the dual black hole thermodynamics.

Findings

Divergences in the partition function are explicitly demonstrated.

The phase of the Pfaffian appears to have little impact on dynamics.

Simulations up to N=12 show promising results for future studies.

Abstract

We perform lattice simulations of N D0-branes at finite temperature in the decoupling limit, namely 16 supercharge SU(N) Yang-Mills quantum mechanics in the 't Hooft limit. At low temperature this theory is conjectured to be dual to certain supergravity black holes. We emphasize that the existence of a non-compact moduli space renders the partition function of the quantum mechanics theory divergent, and we perform one loop calculations that demonstrate this explicitly. In consequence we use a scalar mass term to regulate this divergence and argue that the dual black hole thermodynamics may be recovered in the appropriate large N limit as the regulator is removed. We report on simulations for N up to 5 including the Pfaffian phase, and N up to 12 in the phase quenched approximation. Interestingly, in the former case, where we may calculate this potentially difficult phase, we find that it appears to play little role dynamically over the temperature range tested, which is certainly encouraging for future simulations of this theory.