Enhanced N=8 Supersymmetry of ABJM Theory on R(8) and R(8)/Z(2)

TL;DR

This paper proves that ABJM theory exhibits enhanced N=8 supersymmetry and SO(8) R-symmetry at levels k=1,2 by using monopole operators and rewriting the Lagrangian in an SO(8) invariant form.

Contribution

The authors demonstrate the enhancement of supersymmetry and R-symmetry in ABJM theory at specific levels, providing a new understanding of its symmetry structure.

Findings

Enhanced N=8 supersymmetry at levels k=1,2

Manifest SO(8) invariance of the scalar potential

Identification of new N=2 supersymmetry using monopole operators

Abstract

The ABJM theory refers to superconformal Chern-Simons-matter theory with product gauge group U(L)xU(R) and level +k, -k, respectively. The theory is a candidate for worldvolume dynamics of M2-branes sitting at C(4)/Z(k)k. By utilizing monopole operators, we prove that ABJM theory gets enhanced N=8 supersymmetry and SO(8) R-symmetry at Chern-Simons levels k=1,2. We first show that the ABJM Lagrangian can be written in a manifestly SO(8) invariant form up to certain extra terms. We then show that upon integrating out Chern-Simons gauge fields these extra terms vanish precisely at levels k=1,2. Utilizing monopole operators at these levels, we identify new N=2 supersymmetry. We demonstrate that they combine with the manifest N=6 supersymmetry to close on-shell on N=8 supersymmetry. We finally show that the ABJM scalar potential is SO(8) invariant.