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 divide the partition function of the finite N Yang-Mills theory into two sectors, and show that one of these can be interpreted as a sum of covering maps from closed string world-sheets to the target space, whose covering number is less than N . This provides an asymptotic expansion of 1/N whose large N limit becomes the chiral sector defined by D. Gross and W. Taylor. We also discuss the appearance of non-perturbative corrections which emerge in the other sector of the partition function. 1 [email protected] 2 [email protected]