Thermodynamic potential for compactified bosonic strings

TL;DR

This paper develops a modular-invariant thermodynamic potential for bosonic strings with compactified dimensions, incorporating chemical potentials and examining duality symmetry at one-loop level.

Contribution

It introduces a modular-invariant expression for the thermodynamic potential of compactified bosonic strings including chemical potentials, enhancing understanding of string thermodynamics.

Findings

Duality symmetry in thermodynamic potential analyzed

Modular invariance achieved in the thermodynamic expression

Path integral method used at one-loop level

Abstract

We discuss the inclusion of chemical potentials of the Kaluza-Klein charges in the partition function of the bosonic string with a compactified dimension on a circle. The construction of the thermodynamic potential is achieved by the path integral method at one-loop level. Duality symmetry in the dependence on compactification scale is examined. A modular-invariant expression for the thermodynamic potential is also presented.