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Holomorphic Blocks in 3d

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Recently techniques have been developed to compute the
partition functions of 3d theories with N=2 supersymmetry on curved, compact
spaces, in particular S^3 and S^2xS^1 (the latter giving a supersymmetric
index). I will discuss how both of these partition functions can be decomposed
as products of more fundamental, universal "holomorphic blocks." For
3d gauge theories arising from (auxiliary) 3-manifolds M, these holomorphic
blocks are specific Chern-Simons partition functions on M.