Thermodynamic potential for compactified bosonic strings

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.