On the Witten index of 3d N=2 unitary SQCD with general CS levels

We consider unitary SQCD, a three-dimensional N=2 supersymmetric Chern-Simons-matter theory consisting of one U(N_c)_k,k+lNc 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)×U(1))/ℤ_Nc. 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≠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)×U(N′) gauge group.