Studies of the ABJM Theory in a Formulation with Manifest SU(4) R-Symmetry

TL;DR

This paper analyzes the ABJM superconformal Chern--Simons theory in a formulation with explicit SU(4) R-symmetry, confirming its full superconformal symmetry and rewriting its scalar potential as a sum of squares.

Contribution

It provides a detailed verification of supersymmetry and superconformal symmetry in a manifest SU(4) formulation of the ABJM theory, with a novel recasting of the scalar potential.

Findings

Confirmed complete OSp(6|4) superconformal symmetry.

Verified both Poincare and conformal supersymmetry.

Recast scalar potential as a sum of squares.

Abstract

We examine the three-dimensional N = 6 superconformal Chern--Simons theory with U(N) X U(N) gauge symmetry, which was recently constructed by Aharony, Bergman, Jafferis, and Maldacena (ABJM). Using a formulation with manifest SU(4) R-symmetry and no auxiliary fields, we verify in complete detail both the Poincare supersymmetry and the conformal supersymmetry of the action. Together, these imply the complete OSp(6|4) superconformal symmetry of the theory. The potential, which is sixth order in scalar fields, is recast as a sum of squares.