On ${\mathcal N}=4$ supersymmetry enhancements in three dimensions

TL;DR

This paper introduces a class of 3d theories combining strongly-coupled ${\mathcal N}=4$ systems with ${\mathcal N}=3$ Chern-Simons gauge multiplets, demonstrating conditions under which supersymmetry enhances to ${\mathcal N}=4$, and exploring geometric interpretations via M5-branes.

Contribution

The paper constructs new 3d ${\mathcal N}=4$ theories from coupled systems and identifies specific conditions for supersymmetry enhancement, expanding the landscape of known theories.

Findings

Supersymmetry enhances to ${\mathcal N}=4$ when $1/k_1+1/k_2+1/k_3=0$ in certain Chern-Simons theories.

Some ${\mathcal N}=4$ enhancements are explained through M5-branes on Seifert manifolds.

Introduces a large class of previously unstudied ${\mathcal N}=4$ theories.

Abstract

We introduce a class of 3d theories consisting of strongly-coupled ${\mathcal N}=4$ systems coupled to ${\mathcal N}=3$ Chern-Simons gauge multiplets, which exhibit ${\mathcal N}=4$ enhancements when a peculiar condition on the Chern-Simons levels is met. An example is the $SU(N)^3$ Chern-Simons theory coupled to the 3d $T_N$ theory, which enhances to ${\mathcal N}=4$ when $1/k_1+1/k_2+1/k_3=0$. We also show that some but not all of these ${\mathcal N}=4$ enhancements can be understood by considering M5-branes on a special class of Seifert manifolds. Our construction provides a large class of ${\mathcal N}=4$ theories which have not been studied previously.