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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. This integral in turn allows us to calculate the scaling dimensions of certain protected operators and two-point functions of abelian symmetry currents at arbitrary values of $tau$. Because the underlying theory has conformal symmetry, the current two-point functions tell us the zero temperature conductivity of the Lorentzi
We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddl
The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function. We present this function in the presence of R^2-interactions an
In supersymmetric (SUSY) field theory, there exist configurations which formally satisfy SUSY conditions but are not on original path integral contour. We refer to such configurations as complexified supersymmetric solutions (CSS). In this paper we d
We study $mathcal{N}=1$ supersymmetric three-dimensional Quantum Electrodynamics with $N_f$ two-component fermions. Due to the infra-red (IR) softening of the photon, $ep$-scalar and photino propagators, the theory flows to an interacting fixed point
We study three-dimensional $mathcal{N}=2$ supersymmetric gauge theories on $mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $Sigma_g$. We compute the $mathcal{M}_{g,p}$ supersymmetric partition function and c