Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function

Understand

We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary.

• Our theory has eight real supercharges in the bulk of which four are broken by the presence of the boundary.
• The main result is that the partition function is identical to that of ${\mathcal N}=2$ abelian Chern-Simons theory on a three-sphere coupled to chiral multiplets, but where the quantized Chern-Simons level is replaced by an arbitrary complexified gauge coupling $\tau$.
• The localization reduces the path integral to a single ordinary integral over a real variable.