The String Partition Function for QCD on the Torus

TL;DR

This paper calculates the free energy of the pure glue QCD string on a torus, revealing modular covariance and exact results for multiple genera, with mild singularities at weak coupling.

Contribution

It provides an exact computation of the string free energy in QCD on a torus using modular forms, highlighting duality and covariance properties.

Findings

Exact free energy expressions for genera 1-8

Modular covariance constrains the free energy

Mild singularity in weak coupling limit

Abstract

We study the free energy of the pure glue QCD string with a torus target space and the gauge groups $SU(N)$ and (chiral) $U(N)$. It is highly constrained by a strong/weak gauge coupling duality which results in modular covariance. The string free energy is computed exactly in terms of modular forms for worldsheet genera 1 - 8. It has a surprisingly mild singularity in the weak gauge coupling/small area limit.