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Review of localization for 5d supersymmetric gauge theories

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arxiv 1608.02966 v3 pith:SEDMXC4L submitted 2016-08-09 hep-th math-phmath.MP

Review of localization for 5d supersymmetric gauge theories

classification hep-th math-phmath.MP
keywords gaugegivelocalizationreviewsasaki-einsteinsupersymmetrictheoremstoric
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We give a pedagogical review of the localization of supersymmetric gauge theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological complex resulting from supersymmetry and consider its natural toric deformations with all equivariant parameters turned on. We also give detailed discussion on how the Sasaki-Einstein geometry permeates every aspect of the calculation, from Killing spinor, vanishing theorems to the index theorems.

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