4d $\mathcal{N}=3$ indices via discrete gauging

TL;DR

This paper develops a method to compute superconformal indices for 4d $ =3$ SCFTs obtained from discrete gauging of $ =4$ SYM, revealing new insights into their Coulomb and Higgs branches.

Contribution

It introduces a prescription for discrete gauging at the level of indices and Hilbert series, enabling analysis of higher rank theories and their moduli spaces.

Findings

Coulomb branches of higher rank theories are generally not freely generated.

The method matches known results for rank one $ =3$ theories.

New predictions for moduli space structures of higher rank theories.

Abstract

A class of 4d $\mathcal{N}=3$ SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of $\mathcal{N}=4$ Super Yang-Mills theory. This discrete subgroup contains elements of both the $SU(4)$ R-symmetry group and the $SL(2,\mathbb{Z})$ S-duality group of $\mathcal{N}=4$ SYM. We give a prescription for how to perform the discrete gauging at the level of the superconformal index and Higgs branch Hilbert series. We interpret and match the information encoded in these indices to known results for rank one $\mathcal{N}=3$ theories. Our prescription is easily generalised for the Coloumb branch and the Higgs branch indices of higher rank theories, allowing us to make new predictions for these theories. Most strikingly we find that the Coulomb branches of higher rank theories are generically not-freely generated.