BF theories and group-level duality Original Research Article

It is known that the partition function and correlators of the two-dimensional topological field theory GK(N)/GK(N) on the Riemann surface Σg,s is given by Verlinde numbers, dim Vg,s,K, and that the large K limit of dim Vg,s,K gives Volμs, the volume of the moduli space of flat connections of gauge group G(N) on Σg,s, up to a power of K. Given this relationship, we complete the computation of VolμMs using only algebraic results from conformal field theory. The group-level duality of GK(N) is used to show that if G(N) is a classical group, then limN→∞GK(N)/GK(N) is a BF theory with gauge group G(K). Therefore this limit computes Volμs, the volume of the moduli space of flat connections of gauge group G(K).