Schwarzschild Black Holes from Matrix Theory

TL;DR

This paper demonstrates that Matrix theory compactified on T^3 accurately models the properties of 7+1 dimensional Schwarzschild black holes, including key thermodynamic and geometric features, with a novel approach linking the cutoff to black hole entropy.

Contribution

It provides a new validation of Matrix theory as a description of higher-dimensional black holes using a specific equation of state for SYM theory.

Findings

Matrix theory reproduces black hole energy-entropy relations.

The Hawking temperature and size are correctly modeled.

The cutoff N correlates with black hole entropy.

Abstract

We consider Matrix theory compactified on T^3 and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the energy-entropy relation, the Hawking temperature and the physical size, up to numerical factors of order unity. The most economical description involves setting the cut-off N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional SYM theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.