Schwarzschild Black Holes from Matrix Theory

TL;DR

This work embeds Schwarzschild black holes in seven-plus-one dimensions within Matrix theory by compactifying on T^3 and treating the N-sector as 3+1D N=4 SYM with a conformal equation of state. The authors show that, with N chosen on the order of the black hole entropy, one can reproduce the energy–entropy relation, Hawking temperature, and size up to factors of order unity, and they analyze the regime of validity via a transition to wrapped 3-brane dynamics at low temperature. A key result is that the black hole size scales as (S G_8)^{1/6}, and the Hawking temperature scales inversely with the Schwarzschild radius, consistent with gravitational expectations. The picture also links microscopic 0-brane dynamics and emission to the macroscopic thermodynamics, offering a concrete matrix-theory realization of non-extremal black holes and their Hawking radiation behavior. These findings support the viability of Matrix theory as a non-perturbative framework for describing Schwarzschild black holes in higher dimensions and illuminate how wrapped branes and DLCQ cutoffs govern thermodynamic properties.

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.