From $\mathcal{N}{=}\,4$ Galilean superparticle to three-dimensional non-relativistic $\mathcal{N}{=}\,4$ superfields

TL;DR

This paper constructs and analyzes a non-relativistic $ ext{N}=4$ superparticle model in three dimensions, exploring its symmetries, constraints, and quantization to produce superfields useful for supersymmetric theories.

Contribution

It introduces a new class of $ ext{N}=4$ non-relativistic superparticle actions with linear central charge dependence and studies their quantization and superfield realization.

Findings

Derived the phase space constraints and gauge symmetries of the superparticle model.

Quantized the model to obtain free $ ext{N}=4$ superfields in three dimensions.

Provided a framework for describing non-relativistic $ ext{N}=4$ supersymmetric theories.

Abstract

We consider the general $\mathcal{N}{=}\,4,$ $d{=}\,3$ Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for $\mathcal{N}{=}\,4$ three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic $\kappa$-gauge transformations. The quantization of the model gives rise to the collection of free $\mathcal{N}{=}\,4$, $d{=}\,3$ Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic $\mathcal{N}{=}\,4$ supersymmetric theories.