Quantum states, thermodynamic limits, and entropy inMtheory

Abstract

We discuss the matching of the BPS part of the spectrum for a (super)membrane, which gives the possibility of getting the 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 a large coupling constant is computed by considering M theory on a manifold with a topology ${T}^{2}\ifmmode\times\else\texttimes\fi{}{R}^{9}.$ We argue that the finite temperature partition functions (brane Laurent series for $p\ensuremath{\ne}1)$ associated with the 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 $\stackrel{\ensuremath{\rightarrow}}{p}0$ (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.