TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.085
TI  - On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels
PY  - 2023/09/08
UR  - https://scipost.org/SciPostPhys.15.3.085
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 085
A1  - Closset, Cyril
AU  - Khlaif, Osama
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.3.085,
	title={{On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels}},
	author={Cyril Closset and Osama Khlaif},
	journal={SciPost Phys.},
	volume={15},
	pages={085},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.085},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.085},
}