Quantum States, Thermodynamic Limits and Entropy in M-Theory

TL;DR

This paper explores the thermodynamic properties of M-theory and its relation to string theory, analyzing entropy and finite temperature behavior of branes and membranes across different coupling regimes.

Contribution

It provides a novel analysis of the thermodynamic limits and entropy matching in M-theory and string theory, including finite temperature effects and BPS spectrum matching.

Findings

Entropy of M-theory matches type IIB string theory at small coupling.

Finite temperature partition functions for branes can be analytically continued.

Thermodynamic behavior transitions smoothly to point particle limit.

Abstract

We discuss the matching of the BPS part of the spectrum for (super)membrane, which gives the possibility of getting membrane's results via string calculations. In the small coupling limit of M--theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at large coupling constant is computed by considering M--theory on a manifold with topology ${\mathbb T}^2\times{\mathbb R}^9$. We argue that the finite temperature partition functions (brane Laurent series for $p \neq 1$) associated with BPS $p-$brane spectrum can be analytically continued to well--defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit $p \to 0$ (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.