Quantum State Density and Critical Temperature in M-theory

TL;DR

This paper explores the thermodynamic properties of quantum states in M-theory, linking membrane and string spectra, and analyzing phase transitions and critical temperatures at various coupling strengths.

Contribution

It provides a microscopic interpretation of thermodynamic quantities in M-theory and computes critical temperatures using membrane and string spectrum matching.

Findings

Critical behavior resembles a first order phase transition below Hagedorn temperature

Critical temperature at large coupling is computed for M-theory on specific manifolds

Finite temperature can be incorporated into membrane thermodynamics

Abstract

We discuss the asymptotic properties of quantum states density for fundamental $p-$branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory the critical behavior coincides with the first order phase transition in standard string theory at temperature less than the Hagedorn's temperature $T_H$. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology ${\mathbb R}^9\otimes{mathbb T}^2$. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.