Review of localization for 5d supersymmetric gauge theories

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.

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

References in corpus (6)

• Localization techniques in quantum field theories
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Supersymmetric Gauge Theories on the Five-Sphere
• Holomorphic blocks and the 5d AGT correspondence
• Gluing Nekrasov partition functions
• Matrix models for 5d super Yang-Mills

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• SYM on Quotients of Spheres and Complex Projective Spaces
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
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• Five-dimensional gauge theories on spheres with negative couplings
• On a 5D UV completion of Argyres-Douglas theories
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