  We describe and solve a double scaling limit of large N Yang-Mills theory on
a two-dimensional torus. We find the exact strong-coupling expansion in this
limit and describe its relation to the conventional Gross-Taylor series. The
limit retains only the chiral sector of the full gauge theory and the
coefficients of the expansion determine the asymptotic Hurwitz numbers, in the
limit of infinite winding number, for simple branched coverings of a torus.
These numbers are computed exactly from the gauge theory vacuum amplitude and
shown to coincide with the volumes of the principal moduli spaces of
holomorphic differentials. The string theory interpretation of the double
scaling limit is also described.
