SU(2|2) supersymmetric mechanics

TL;DR

This paper introduces a new class of non-relativistic ${ m extbf{N}=8}$ supersymmetric mechanics based on the supergroup $SU(2|2)$, develops superfield techniques, and constructs actions for various multiplets, including quantization of the simplest model.

Contribution

It presents the first construction of ${ m extbf{N}=8}$ supersymmetric mechanics with $SU(2|2)$ symmetry, including superfield formulations and analysis of multiplets.

Findings

Constructed superfield actions for ${ m extbf{N}=8}$ multiplets

Identified mass oscillator terms related to deformation parameter

Performed quantization of the simplest model

Abstract

We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various worldline $SU(2|2)$ superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell $SU(2|2)$ multiplets $({\bf 3,8,5})$, $({\bf 4,8,4})$ and $({\bf 5,8,3})$, we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group $OSp(4^*|4)$ in the conformal cases. For the simplest $({\bf 5, 8, 3})$ model the quantization is performed.