S-duality of the 3d Chern-Simons matter gauge theory with fundamental hypermultiplets

3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality

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 or for supersymmetry is spontaneously broken, which is in accord with the fact that the partition function vanishes.We comment on the magnetic description dual to the so-called ``ugly''theory, where the usual decoupled sector is still interacting with others.We argue that the ``ugly-good''duality (which corresponds to the limit in our setup) is closely related to the s-duality of the 4d superconformal gauge theory with fundamentalhypermultiplets.