3d $$ \mathcal{N} $$ = 3 generalized Giveon-Kutasov duality

Abstract

Abstract We generalize the Giveon-Kutasov duality for the 3d $$ \mathcal{N} $$ N = 3 U(N)k,k+nN Chern-Simons matter gauge theory with F fundamental hypermultiplets by introducing SU(N) and U(1) Chern-Simons levels differently. We study the supersymmetric partition functions and the superconformal indices of the duality, which supports the validity of the duality proposal. From the duality, we can map out the low-energy phases: for example, confinement appears for F + k − N = −n = 1 or N = 2F = k = −n = 2. For F + k − N < 0, supersymmetry is spontaneously broken, which is in accord with the fact that the partition function vanishes. In some cases, the theory shows supersymmetry enhancement to 3d $$ \mathcal{N} $$ N = 4. For k = 0, we comment on the magnetic description dual to the so-called “ugly” theory, where the usual decoupled sector is still interacting with others for n ≠ 0. We argue that the SU(N)0 “ugly-good” duality (which corresponds to the n → ∞ limit in our setup) is closely related to the S-duality of the 4d $$ \mathcal{N} $$ N = 2 SU(N) superconformal gauge theory with 2N fundamental hypermultiplets. By reducing the number of flavors via real masses, we suggest possible ways to flow to the “bad” theories.