Mellin-Barnes Representation for the Genus-g Finite Temperature String Theory

TL;DR

This paper develops a Mellin-Barnes representation for genus-g string free energy, revealing that open bosonic string interactions do not alter the Hagedorn temperature, while spinor sectors exhibit a genus-dependent critical temperature.

Contribution

It introduces a Mellin-Barnes framework for genus-g string free energy and analyzes the impact of interactions and spinor sectors on the critical temperature.

Findings

Open bosonic string interactions do not change the Hagedorn temperature.

Spinor sectors have a genus-dependent critical temperature.

Periodic structures in the string sectors are briefly discussed.

Abstract

The Mellin-Barnes representation for the free energy of the genus-$g$ string is constructed. It is shown that the interactions of the open bosonic string do not modify the critical (Hagedorn) temperature. However,for the sectors having a spinor structure, the critical temperature exists also for all $g$ and depends on the windings. The appearance of a periodic structure is briefly discussed.