Global Properties of Supersymmetric Theories and the Lens Space

TL;DR

This paper calculates the supersymmetric partition function on lens spaces for 4d gauge theories, revealing how global gauge group properties and discrete parameters influence dualities like Seiberg and S-dualities.

Contribution

It provides explicit computations of the lens space index for theories with non simply-connected groups, highlighting the role of global properties and discrete theta angles in dualities.

Findings

Partition function distinguishes different global gauge group structures.

Explicit analysis of N=1 so(N_c) Seiberg dualities.

Explicit analysis of N=4 su(N_c) S-dualities.

Abstract

We compute the supersymmetric partition function on L(r,1)xS^1, the lens space index, for 4d gauge theories related by supersymmetric dualities and involving non simply-connected groups. This computation is sensitive to the global properties of the underlying gauge group and to discrete theta angle parameters and thus distinguishes versions of dualities differing by such. We explicitly discuss N=1 so(N_c) Seiberg dualities and N=4 su(N_c) S-dualities.