SU(2|1) mechanics and harmonic superspace

TL;DR

This paper develops a harmonic superspace framework for SU(2|1) supersymmetric mechanics, constructs supermultiplets and actions, and explores their superconformal properties and quantum spectra.

Contribution

It introduces a deformed harmonic superspace for SU(2|1), describes off-shell supermultiplets, and analyzes superconformal invariance and quantum states in this setting.

Findings

Invariant actions exist for both (4,4,0) multiplets, but Wess-Zumino terms are only for one, showing non-equivalence.

Superconformal actions invariant under D(2,1;α) are identified, with infinite-dimensional supersymmetry.

Explicit quantum mechanical examples reveal SU(2|1) representation contents of states.

Abstract

We define the worldline harmonic SU(2|1) superspace and its analytic subspace as a deformation of the flat N=4, d=1 harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell (4,4,0) SU(2|1) supermultiplets is developed and the corresponding invariant actions are presented, as well as the relevant classical and quantum supercharges. Whereas the \sigma-model actions exist for both types of the (4,4,0) multiplet, the invariant Wess-Zumino term can be defined only for one of them, thus demonstrating non-equivalence of these multiplets in the SU(2|1) case as opposed to the flat N=4, d=1 supersymmetry. A superconformal subclass of general SU(2|1) actions invariant under the trigonometric-type realizations of the supergroup D(2,1;\alpha) is singled out. The superconformal Wess-Zumino actions possess an infinite-dimensional supersymmetry forming the centerless N=4 super Virasoro algebra. We solve a few simple instructive examples of the SU(2|1) supersymmetric quantum mechanics of the (4,4,0) multiplets and reveal the SU(2|1) representation contents of the corresponding sets of the quantum states.