On central charges and the entropy in matrix theory

TL;DR

This paper explores how the matrix model of M-theory can be used to compute black hole entropy and microstates, drawing analogies with BPS black holes and proposing a gauge theory for the 11-dimensional KK monopole.

Contribution

It introduces a method to calculate matrix-entropy for specific configurations and proposes a new gauge theory to count microstates in matrix theory.

Findings

Matrix-entropy for 2x2x2 configuration matches expected black hole entropy.

Matrix-entropy for 5x5x5 configuration relates to 5D string microstates.

Proposes gauged world volume theory of 11D KK monopole for microstate counting.

Abstract

The Bekenstein-Hawking entropy of BPS black holes can be obtained as the minimum of the mass (= largest central charge). In this letter we investigate the analog procedure for the matrix model of M-theory. Especially we discuss the configurations: (i) $2 \times 2 \times 2$ corresponding to the 5-d black hole and (ii) the $5 \times 5 \times 5$ configuration yielding the 5-d string. After getting their matrix-entropy, we discuss a way of counting of microstates in matrix theory. As Yang Mills field theory we propose the gauged world volume theory of the 11-d KK monopole.