Mass-deformed $\mathcal{N} = 3$ Supersymmetric Chern-Simons-Matter Theory

TL;DR

This paper explicitly constructs the mass-deformed $ =3$ supersymmetric $U(N)$ Chern-Simons-Matter theory, providing a detailed action form and demonstrating the unique supersymmetry-preserving mass deformation.

Contribution

It presents the explicit form of the mass-deformed $ =3$ supersymmetric Chern-Simons-Matter theory in $ =1$ superspace, including the unique triplet mass deformation term.

Findings

Explicit action for mass-deformed $ =3$ theory provided

Unique triplet mass deformation term identified

Constructed in $ =1$ superspace with fundamental and anti-fundamental superfields

Abstract

The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $\mathcal{N} = 3$ supersymmetry. In this short note, we provide the explicit form of the action for the mass-deformed $\mathcal{N} = 3$ supersymmetric $U(N)$ Chern-Simons-Matter theory. The theory admits a unique triplet mass deformation term consistent with supersymmetry. We explicitly construct the mass-deformed $\mathcal{N} = 3$ theory in $\mathcal{N} = 1$ superspace using a fundamental and an anti-fundamental superfield.