String theoretical interpretation for finite N Yang-Mills theory in two dimensions

We discuss the equivalence between a string theory and the two-dimensional Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which can be interpreted as a sum of covering maps from closed string worldsheets to the target space, whose covering number is less than N. This gives an asymptotic expansion of 1/N whose large N limit becomes the chiral sector defined by Gross and Taylor. We also discuss that the residual part of the partition function provides the nonperturbative corrections to the perturbative expansion.