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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 correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called fibering operator on $S^2 times S^1$ with a topological twist. More generally, we show that the 3d $mathcal{N}=2$ supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on $mathcal{M}_{g,p}$ are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimensional supersymmetric dualities.
We derive the partition function of 5d ${cal N}=1$ gauge theories on the manifold $S^3_b times Sigma_{frak g}$ with a partial topological twist along the Riemann surface, $Sigma_{frak g}$. This setup is a higher dimensional uplift of the two-dimensio
Localization methods have produced explicit expressions for the sphere partition functions of (2,2) superconformal field theories. The mirror symmetry conjecture predicts an IR duality between pairs of Abelian gauged linear sigma models, a class of w
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically calculate the q
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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 b