A New Duality Between $\mathcal{N}=8$ Superconformal Field Theories in Three Dimensions

TL;DR

This paper introduces a new duality between two three-dimensional $ ext{N}=8$ superconformal theories, supported by matching moduli spaces, indices, partition functions, and BPS operator coefficients.

Contribution

It proposes a novel duality between the $U(3)_1 imes U(3)_{-1}$ ABJM theory and a product of BLG and free scalar-fermion theories, with supporting evidence from multiple checks.

Findings

Matching moduli spaces between the theories

Agreement of superconformal indices

Consistent $S^3$ partition functions

Abstract

We propose a new duality between two 3d $\mathcal{N}=8$ superconformal Chern-Simons-matter theories: the $U(3)_1 \times U(3)_{-1}$ ABJM theory and a theory consisting of the product between the $\left(SU(2)_3\times SU(2)_{-3}\right)/\mathbb{Z}_2$ BLG theory and a free ${\cal N} = 8$ theory of eight real scalars and eight Majorana fermions. As evidence supporting this duality, we show that the moduli spaces, superconformal indices, $S^3$ partition functions, and certain OPE coefficients of BPS operators in the two theories agree.