Localization on round sphere revisited

Abstract

We consider supersymmetric gauge theories on round 3-sphere with a certain background gauge field. The Lagrangians break the usual symmetry because the background gauge field which we have turned on violates the isometry. In order to maintain the supersymmetry, we choose unfamiliar charged Killing spinors as N = 2 SUSY parameters. We perform localization calculous within this setup and find the double sine function as we expected. We comment on more direct relationship between theories on round sphere and squashed sphere via Weyl transformation.

17 pages. Weyl rescaling and Wilson loop discussions added. reference added

References in corpus (6)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Notes on SUSY Gauge Theories on Three-Sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
• The Geometry of Supersymmetric Partition Functions
• On the moduli space of elliptic Maxwell-Chern-Simons theories
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry

Cited by in corpus (15)

• The Geometry of Supersymmetric Partition Functions
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Higgs branch localization of 3d N=2 theories
• Direct derivation of "mirror" ABJ partition function
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole
• Factorization of S^3/Z_n partition function
• An introduction to supersymmetric field theories in curved space
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Supersymmetric Rényi Entropy in Two Dimensions
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• A review on SUSY gauge theories on $S^3$
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• N=1 Chern-Simons-matter theory and localization