SciPost Submission Page
On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels
by Cyril Closset, Osama Khlaif
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Cyril Closset |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2305.00534v3 (pdf) |
| Date accepted: | 2023-07-18 |
| Date submitted: | 2023-07-11 06:56 |
| Submitted by: | Closset, Cyril |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We consider unitary SQCD, a three-dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-matter theory consisting of one $U(N_c)_{k, k+l N_c}$ vector multiplet coupled to $n_f$ fundamental and $n_a$ antifundamental chiral multiplets, where $k$ and $l$ parameterise generic CS levels for $U(N_c)=(SU(N_c)\times U(1))/\mathbb{Z}_{N_c}$. We study the moduli space of vacua of this theory with $n_a=0$, for generic values of the parameters $N_c, k, l, n_f$ and with a non-zero Fayet-Ilopoulos parameter turned on. We uncover a rich pattern of vacua including Higgs, topological and hybrid phases. This allows us to derive a closed-form formula for the flavoured Witten index of unitary SQCD for any $n_f\neq n_a$, generalising previously known results for either $l=0$ or $n_f=n_a$. Finally, we analyse the vacuum structure of recently proposed infrared-dual gauge theories and we match vacua across the dualities, thus providing intricate new checks of those dualities. Incidentally, we also discuss a seemingly new level/rank duality for pure CS theories with $U(N)\times U(N')$ gauge group.
List of changes
We corrected various typos, including all the ones pointed out by the referees. We also added various small clarifications to address the suggestions and concerned raised in the reports. Here is a list of the most salient changes:
1) We added equation (1.2) and clarified the discussion around it.
2) We added a comment about future directions at the end of the intro.
3) We added footnote 4 about the flavour group.
4) We clarified the notation above eq.(3.9)
5) We clarified why we have some (S)U(p)_0 groups appearing on page 18.
Published as SciPost Phys. 15, 085 (2023)