N=4, d=3 nonlinear electrodynamics

TL;DR

This paper develops a new nonlinear vector supermultiplet for three-dimensional N=4 supersymmetry, constructs a sigma-model action, and derives a dual scalar form leading to a hyper-Kähler sigma-model.

Contribution

It introduces a novel off-shell nonlinear vector supermultiplet for 3D N=4 supersymmetry and formulates its sigma-model action with dualization to a hyper-Kähler sigma-model.

Findings

Constructed a new off-shell nonlinear vector supermultiplet.

Presented the general sigma-model action for the nonlinear supermultiplet.

Derived a dual scalar action describing a hyper-Kähler sigma-model.

Abstract

We construct a new off-shell $\mathcal{N}{=}4$, $d{=}3$ nonlinear vector supermultiplet. The irreducibility constraints for the superfields leave in this supermultiplet the same component content as in the ordinary linear vector supermultiplet. We present the most general sigma-model type action for the $\mathcal{N}{=}4$, $d{=}3$ electrodynamics with the nonlinear vector supermultiplet, which despite the nonlinearity of the supermultiplet may be written as an integral over a chiral superspace. This action share the most important properties with its linear counterpart. We also perform the dualization of the vector component into a scalar one and find the corresponding $\mathcal{N}{=}4$, $d{=}3$ supersymmetric action which describes new hyper-K\"ahler sigma-model in the bosonic sector.