ABJM models in N=3 harmonic superspace

TL;DR

This paper develops an N=3 harmonic superspace formulation of the ABJM model, revealing its supersymmetry structure, gauge interactions, and scalar potential, and extends it to related models with enhanced symmetries.

Contribution

It provides the first classical superfield action of the ABJM model in N=3 harmonic superspace, including its supersymmetry, gauge interactions, and scalar potential, and explores generalizations.

Findings

Superfield action involves hypermultiplets and Chern-Simons gauge superfields.

The scalar potential of ABJM naturally emerges after eliminating auxiliary fields.

Enhanced N=8 supersymmetry and SO(8) R-symmetry are demonstrated for SU(2)xSU(2) case.

Abstract

We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three out of six supersymmetries are realized off shell while the other three mix the superfields and close on shell. The superfield action involves two hypermultiplet superfields in the bifundamental representation of the gauge group and two Chern-Simons gauge superfields corresponding to the left and right gauge groups. The N=3 superconformal invariance allows only for a minimal gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar potential of ABJM emerges after the elimination of auxiliary fields. Besides the original U(N)xU(N) ABJM model, we also construct N=3 superfield formulations of some generalizations. For the SU(2)xSU(2) case we give a simple superfield proof of its enhanced N=8 supersymmetry and SO(8) R-symmetry.