Squashing and supersymmetry enhancement in three dimensions

Abstract

We consider mass-deformed theories with $\mathcal{N}\ge 2$ supersymmetry on round and squashed three-spheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently observed squashing independence of the partition function of mass-deformed ABJ(M) theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.

15+9 pages

References in corpus (4)

• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Conformal field theories on deformed spheres, anomalies, and supersymmetry
• $\mathcal{N}=2$ Supergravity in $D=4,5,6$ Dimensions
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories

Cited by in corpus (6)

• Large $N$ Partition Functions of the ABJM Theory
• One-Dimensional Sectors From the Squashed Three-Sphere
• Dualities and loops on squashed $S^3$
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• The Holographic Contributions to the Sphere Free Energy