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

We generalize the Giveon-Kutasov duality for 3d $\mathcal{N}=3$ $U(N)_{k,k+nN}$ Chern-Simons matter gauge theory with $F$ fundamental hypermultiplets by introducing $SU(N)$ and $U(1)$ levels differently. study supersymmetric partition functions superconformal indices of duality, which supports validity proposal. From we can map out low-energy phases: For example, confinement appears $F+k-N=-n=1$ or $N=2F=k=-n=2$. $F+k-N<0$, supersymmetry is spontaneously broken, in accord fact that function vanishes. In some cases, shows enhancement to $\mathcal{N}=4$. $k=0$, comment on magnetic description dual so-called "ugly" theory, where usual decoupled sector still interacting others $n \neq 0$. argue $SU(N)_0$ "ugly-good" (which corresponds \rightarrow \infty$ limit our setup) closely related S-duality 4d $\mathcal{N}=2$ $2N$ hypermultiplets. By reducing number flavors via real masses, suggest possible ways flow "bad" theories.