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

TL;DR

This paper extends the Giveon-Kutasov duality to 3d $ =3$ $U(N)$ Chern-Simons theories with varied levels, analyzing their phases, supersymmetry properties, and connections to 4d dualities through partition functions and indices.

Contribution

It introduces a generalized duality framework for 3d $ =3$ theories with different Chern-Simons levels and explores their phase structure and supersymmetry enhancements.

Findings

Support for the duality via partition functions and indices

Identification of confinement and supersymmetry breaking conditions

Connection to 4d S-duality in certain limits

Abstract

We generalize the Giveon-Kutasov duality for the 3d $\mathcal{N}=3$ $U(N)_{k,k+nN}$ Chern-Simons matter gauge theory with $F$ fundamental hypermultiplets by introducing $SU(N)$ and $U(1)$ 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 $\mathcal{N}=4$. 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 $n \neq 0$. We argue that the $SU(N)_0$ "ugly-good" duality (which corresponds to the $n \rightarrow \infty$ limit in our setup) is closely related to the S-duality of the 4d $\mathcal{N}=2$ $SU(N)$ 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.