Notes on Supersymmetry Enhancement of ABJM Theory

TL;DR

This paper investigates how monopole operators can enhance the supersymmetry of ABJM theory from ${ m N}=6$ to ${ m N}=8$ for specific gauge groups and levels, revealing new symmetry structures.

Contribution

It demonstrates supersymmetry enhancement in ABJM theory using monopole operators, extending understanding of supersymmetry in gauge theories with Chern-Simons matter content.

Findings

Supersymmetry enhances from ${ m N}=6$ to ${ m N}=8$ for $k=1,2$

Monopole operators are key to supersymmetry enhancement

Condition for supersymmetry enhancement in U($N$)$ imes$U($N$) theories

Abstract

We study the supersymmetry enhancement of ABJM theory. Starting from a ${\cal N}=2$ supersymmetric Chern-Simons matter theory with gauge group U(2)$\times$U(2) which is a truncated version of the ABJM theory, we find by using the monopole operator that there is additional ${\cal N}=2$ supersymmetry related to the gauge group. We show this additional supersymmetry can combine with ${\cal N}=6$ supersymmetry of the original ABJM theory to an enhanced ${\cal N}=8$ SUSY with gauge group U(2)$\times$U(2) in the case $k=1,2$. We also discuss the supersymmetry enhancement of the ABJM theory with U($N$)$\times$U($N$) gauge group and find a condition which should be satisfied by the monopole operator.