A review on SUSY gauge theories on $S^3$

Abstract

This is the 9th article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. We review the exact computations in 3D N=2 supersymmetric gauge theories on the round or squashed $S^3$ and the relation between 3D partition functions and 4D superconformal indices.

arXiv comment32 pages, see also overview article arXiv:1412.7145. v2: preprint number updated (no changes in the content)

References in corpus (24)

• N=2 dualities
• An Index for 4 dimensional Super Conformal Theories
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• SUSY Gauge Theories on Squashed Three-Spheres
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The complete superconformal index for N=6 Chern-Simons theory
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• The Geometry of Supersymmetric Partition Functions
• N=2 supersymmetric theories on squashed three-sphere
• Supersymmetry on Curved Spaces and Holography
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Relation between the 4d superconformal index and the S^3 partition function
• The Chern-Simons Coefficient in Supersymmetric Yang-Mills Chern-Simons Theories
• Calculating the Superconformal Index and Seiberg Duality
• S^3/Z_n partition function and dualities
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Chern-Simons theory on L(p,q) lens spaces and Localization
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Exact results for vortex loop operators in 3d supersymmetric theories
• Localization on round sphere revisited
• From Liouville Theory to the Quantum Geometry of Riemann Surfaces

Cited by in corpus (9)

• Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS${}_5$ black holes
• Modular invariance on $S^1\times S^3$ and circle fibrations
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Localization principle in SUSY gauge theories
• Localization and Non-Renormalization in Chern-Simons Theory
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• New Pentagon Identities Revisited
• Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
• N=(4,4) Vector Multiplets on Curved Two-Manifolds