Global Properties of Supersymmetric Theories and the Lens Space

Abstract

We compute the supersymmetric partition function on $${L(r,1)\times \mathbb{S}^1}$$ , 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 $${\mathcal{N}=1}$$ so(N c ) Seiberg dualities and $${\mathcal{N}=4\,su(N_c)}$$ S-dualities.