Hagedorn divergences and tachyon potential

TL;DR

This paper analyzes the critical behavior of string theory near the Hagedorn temperature, showing how divergences can be resummed and related to the effective potential for the thermal scalar, with implications for AdS/CFT correspondence.

Contribution

It introduces a double scaling limit to smooth Hagedorn divergences and connects the string theory behavior to boundary Yang-Mills theory via vortex contributions.

Findings

Hagedorn divergences can be resummed using double scaling limits.

The effective potential for the thermal scalar can be extracted from these limits.

Yang-Mills free energy contains vortex contributions related to string theory boundaries.

Abstract

We consider the critical behavior for a string theory near the Hagedorn temperature. We use the factorization of the worldsheet to isolate the Hagedorn divergences at all genera. We show that the Hagedorn divergences can be resummed by introducing double scaling limits, which smooth the divergences. The double scaling limits also allow one to extract the effective potential for the thermal scalar. For a string theory in an asymptotic anti-de Sitter (AdS) spacetime, the AdS/CFT correspondence implies that the critical Hagedorn behavior and the relation with the effective potential should also arise from the boundary Yang-Mills theory. We show that this is indeed the case. In particular we find that the free energy of a Yang-Mills theory contains ``vortex'' contributions at finite temperature. Yang-Mills Feynman diagrams with vortices can be identified with contributions from boundaries of moduli space on the string theory side.