5D SYM on 3D Deformed Spheres

Abstract

We reconsider the relation of superconformal indices of superconformal field theories of class S with five-dimensional N=2 supersymmetric Yang-Mills theory compactified on the product space of a round three-sphere and a Riemann surface. We formulate the five-dimensional theory in supersymmetric backgrounds preseving N=2 and N=1 supersymmetries and discuss a subtle point in the previous paper concerned with the partial twisting on the Riemann surface. We further compute the partition function by localization of the five-dimensional theory on a squashed three-sphere in N=2 and N=1 supersymmetric backgrounds and on an ellipsoid three-sphere in an N=1 supersymmetric background.

101 pages

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Cited by in corpus (9)

• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• 5d Partition Functions with A Twist
• A slow review of the AGT correspondence
• Surface defects as transfer matrices
• The 5d Superconformal Index at Large $N$ and Black Holes
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions