3d superconformal indices and isomorphisms of M2-brane theories

TL;DR

This paper tests isomorphisms between different M2-brane theories by comparing their superconformal indices, revealing conditions under which these theories are equivalent, and exploring the role of moduli spaces and coprimality.

Contribution

It provides a detailed comparison of superconformal indices for various M2-brane theories, establishing conditions for their isomorphisms based on coprimality of parameters.

Findings

ABJM and (SU(N)xSU(N))/Z_N theories are isomorphic if N and k are coprime.

Superconformal indices match for certain theories, confirming predicted isomorphisms.

Some theories with identical moduli spaces are not isomorphic, indicating subtle differences.

Abstract

We test several expected isomorphisms between the U(N)xU(N) ABJM theory and (SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their superconformal indices. From moduli space analysis, it is expected that this equivalence can hold if and only if the rank N and Chern-Simons level k are coprime. We also calculate the index of the ABJ theory and investigate whether some theories with identical moduli spaces are isomorphic or not.