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

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.

1 + 39 pages; v2: minor corrections in few formulas and many language corrections without any impact on the results; one reference and two footnotes added

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Cited by in corpus (1)

• Superfield approach to higher derivative N=1 superconformal mechanics