Physics Group Meeting

We use the "lens space index", i.e., the partition function on S^3/Z_r x S^1, to study certain properties of four dimensional gauge theories related to the global structure of the gauge group. We show that the lens space index, unlike the ordinary supersymmetric index, can distinguish gauge theories with the same Lie algebra but differing in the global form of the gauge group, and is also sensitive to certain "discrete theta angles" which one may include in theories with non-simply connected gauge groups. This is used to provide new tests of SO(N) Seiberg duality and N=4 SU(N) S-duality, in particular, to check how this global data is mapped under duality. We also comment on surface operators present in such theories, and their relation to discrete electric and magnetic flux sectors.