Harmonic Superspace Gaugeon Formalism for the ABJM Theory

TL;DR

This paper explores the ABJM theory within harmonic superspace, analyzing gauge and BRST symmetries, and demonstrating the unitarity of the S-matrix in this formalism.

Contribution

It introduces a harmonic superspace formulation of the ABJM theory with manifest $ abla=3$ supersymmetry and studies its gaugeon and BRST symmetries.

Findings

BRST symmetry projects out physical states

S-matrix evolution is shown to be unitary

Harmonic superspace parameterization with $SU(2)/U(1)$

Abstract

In this paper we will analyse the ABJM theory in harmonic superspace. The harmonic superspace variables will be parameterized by the coset $SU(2)/U(1)$ and thus will have manifest $\mathcal{N} =3$ supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical sub-space from the total Hilbert space. We will also show that the evolution of the $\mathcal{S}$-matrix is unitary for this ABJM theory in harmonic superspace.