Toward Holographic Reconstruction of Bulk Geometry from Lattice Simulations

TL;DR

This paper demonstrates a method to reconstruct bulk black hole geometry from lattice simulations of gauge theories, providing quantitative insights into holography and black hole physics.

Contribution

It introduces a lattice Monte Carlo approach to probe black hole geometry via gauge theory D-brane interactions, validated in a matrix model dual to a black zero-brane.

Findings

Method successfully reconstructs bulk geometry in high temperature regime

Quantitative agreement with theoretical predictions

Potential for exploring quantum gravity phenomena

Abstract

A black hole described in $SU(N)$ gauge theory consists of $N$ D-branes. By separating one of the D-branes from others and studying the interaction between them, the black hole geometry can be probed. In order to obtain quantitative results, we employ the lattice Monte Carlo simulation. As a proof of the concept, we perform an explicit calculation in the matrix model dual to the black zero-brane in type IIA string theory. We demonstrate this method actually works in the high temperature region, where the stringy correction is large. We argue possible dual gravity interpretations.