N=2 SUSY gauge theories on S^4

Abstract

We review exact results in N=2 supersymmetric gauge theories defined on S^4 and its deformation. We first summarize the construction of rigid SUSY theories on curved backgrounds based on off-shell supergravity, then explain how to apply localization principle to supersymmetric path integrals. Closed formulae for partition function as well as expectation values of non-local BPS observables are presented.

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 (14)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Notes on SUSY Gauge Theories on Three-Sphere
• Sphere Partition Functions and the Zamolodchikov Metric
• Instanton counting with a surface operator and the chain-saw quiver
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Supersymmetric Rényi Entropy in Five Dimensions
• Localization and AdS/CFT Correspondence
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• An introduction to supersymmetric field theories in curved space
• A brief review of the 2d/4d correspondences
• Review of localization in geometry
• W-algebras and surface operators in N=2 gauge theories

Cited by in corpus (17)

• Localization techniques in quantum field theories
• The supersymmetric index in four dimensions
• Spin Impurities, Wilson Lines and Semiclassics
• Localization and AdS/CFT Correspondence
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• A slow review of the AGT correspondence
• Holomorphic blocks and the 5d AGT correspondence
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• Supersymmetric localization in two dimensions
• Introduction to localization in quantum field theory
• An introduction to supersymmetric field theories in curved space
• A brief review of the 2d/4d correspondences
• Review of localization in geometry
• Duality and Mock Modularity
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview