Chern-Simons theory in the SO(5)/U(2) harmonic superspace

TL;DR

This paper develops a superspace formulation for D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates, revealing supermultiplets that include a Chern-Simons gauge field and auxiliary fields, with an action invariant under N=6 conformal supersymmetry.

Contribution

It introduces a novel harmonic superspace approach for D=3, N=5 supersymmetry, enabling the construction of an invariant superfield action with enhanced N=6 symmetry.

Findings

Supermultiplets include a 3D gauge Chern-Simons field.

The superfield action is invariant under N=6 conformal supersymmetry.

Harmonic coordinates facilitate the decomposition of superfields.

Abstract

We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates. Three analytic N=5 gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates. Decomposition of these superfields in Grassmann and harmonic coordinates yields infinite-dimensional supermultiplets including a three-dimensional gauge Chern-Simons field and auxiliary bosonic and fermionic fields carrying SO(5) vector indices. The superfield action of this theory is invariant with respect to D=3, N=6 conformal supersymmetry realized on N=5 superfields.