Euclidean Path Integral, D0-Branes and Schwarzschild Black Holes in Matrix Theory

TL;DR

This paper constructs a Euclidean path integral in Matrix theory with D0-branes as background, deriving mass and entropy that match 11D Schwarzschild black hole properties, linking Euclidean time period to Hawking temperature.

Contribution

It introduces a novel Euclidean path integral approach in Matrix theory with D0-branes, connecting black hole thermodynamics to Matrix theory parameters.

Findings

Mass and entropy match 11D Schwarzschild black hole properties

Euclidean time period relates to Hawking temperature

Entropy proportional to the number of Matrix theory partons

Abstract

The partition function in Matrix theory is constructed by Euclidean path integral method. The D0-branes, which move around in the finite region with a typical size of Schwarzschild radius, are chosen as the background. The mass and entropy of the system obtained from the partition function contain the parameters of the background. After averaging the mass and entropy over the parameters, we find that they match the properties of 11D Schwarzschild black holes. The period $\b$ of Euclidean time can be identified with the reciprocal of the boosted Hawking temperature. The entropy $S$ is shown to be proportional to the number $N$ of Matrix theory partons, which is a consequence of the D0-brane background.