Squashing and supersymmetry enhancement in three dimensions

TL;DR

This paper investigates how mass deformations in 3D supersymmetric theories on squashed spheres can lead to supersymmetry enhancement at specific values, simplifying partition functions and revealing new theoretical insights.

Contribution

It demonstrates supersymmetry enhancement at special mass values on squashed spheres and explains partition function simplifications via supergravity embeddings and geometric equivalences.

Findings

Supersymmetry is enhanced at specific mass deformations.

Partition functions simplify and become independent of squashing at these points.

The results explain observed invariances in mass-deformed ABJ(M) theory.

Abstract

We consider mass-deformed theories with ${\cal N}\geq2$ 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.