Review of localization for 5d supersymmetric gauge theories
Jian Qiu, Maxim Zabzine
TL;DR
This paper reviews the application of localization techniques to 5d supersymmetric gauge theories on toric Sasaki-Einstein manifolds, emphasizing geometric and algebraic structures involved.
Contribution
It provides a comprehensive pedagogical overview of localization in 5d supersymmetric gauge theories, including construction of the cohomological complex and effects of toric deformations.
Findings
Construction of the cohomological complex from supersymmetry
Analysis of toric deformations with equivariant parameters
Detailed discussion of Sasaki-Einstein geometry's role in calculations
Abstract
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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