SciPost Submission Page
Squashing and supersymmetry enhancement in three dimensions
by Joseph Minahan, Usman Naseer, Charles Thull
Submission summary
As Contributors:  Charles Thull 
Arxiv Link:  https://arxiv.org/abs/2107.07151v2 (pdf) 
Date accepted:  20211201 
Date submitted:  20211117 13:31 
Submitted by:  Thull, Charles 
Submitted to:  SciPost Physics 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We consider massdeformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed threespheres. 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 massdeformed ABJ(M) theory on the ellipsoid. We provide further examples of such simplification for various $3d$ supersymmetric theories.
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Author comments upon resubmission
List of changes
1. We use more precise language on page 1 as advocated by the first referee.
2. We generalized our discussions so that they are now applicable to ABJ(M) theory.
3. We mention the $N_f$ model at the end of paragraph 5 of the introduction, as well as in the last paragraph of the introduction.
4. We added the frame for the ellipsoid as eq. (2.29).
5. We added a footnote on the gamma matrix convention to equation (2.1).
6. We added a comment on twisted multiplets in the paragraph before (A.6).
7. We fixed typos and changed the notation in appendix A to clarify various expressions. The simplified oneloop determinants for the $N=4$ vector and hyper multiplets are now given in eq. (A.6) through (A.9).
8. In the second to last paragraph of the introduction we have outlined the logic of the paper which addresses the referee’s remark regarding Qexactness.
Apart from the above changes directly related to the referees’ concerns we have taken the opportunity to fix several typos and make improvements to the draft. The significant changes are listed below.
1. We added a footnote on contracting spinors to eq. (2.6).
2. We added a note on $\mu=\io\frac{b+b^{1}}/2$ after (4.20).
3. In (A.3) and the following equations we corrected the charge that couples to $\mu$ as the flavor charge $F$.
4. We added expressions for the ${\cal N}=4$ vector oneloop partition function, explaining the squashing independence.
5. We added a comment on the flavor charge of the ${\cal N}=4$ multiplet constituents.
6. We revised the $N_f$model in section (A.2).