  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.
