BF THEORIES AND GROUP-LEVEL DUALITY

It is known that the partition function and correlators of the two-dim ensional topological field theory G(K)(N)/G(K)(N) on the Riemann surfa ce Sigma(g,s) is given by Verlinde numbers, dim V-g,V-s,V-K, and that the large K limit of dim V-g,V-s,V-K gives Vol M(s), the volume of the moduli space of flat connections of gauge group G(N) on Sigma(g,s), u p to a power of K. Given this relationship, we complete the computatio n of Vol M(s) using only algebraic results from conformal held theory. The group-level duality of GK(N) is used to show that if G(N) is a cl assical group, then kim(N-->infinity) G(K)(N)/G(K)(N) is a BF theory w ith gauge group G(K). Therefore this limit computes Vol M'(s), the vol ume of the moduli space of flat connections of gauge group G(K).