N=4 Supersymmetric Mechanics in Harmonic Superspace

TL;DR

This paper develops a harmonic superspace framework for N=4, d=1 supersymmetric mechanics, providing new superfield formulations, actions, and insights into superconformal invariance and potential generalizations.

Contribution

It introduces a novel harmonic superspace formulation for N=4 supersymmetric quantum mechanics, enabling off-shell superfield actions and revealing superconformal invariance properties.

Findings

Constructed superfield actions with sigma-model and superpotential parts.

Demonstrated off-shell superpotentials in analytic superspace.

Showed invariance under the superconformal group D(2,1;α).

Abstract

We define N=4, d=1 harmonic superspace HR^{1+2|4} with an SU(2)/U(1) harmonic part, SU(2) being one of two factors of the R-symmetry group SU(2)xSU(2) of N=4, d=1 Poincar\'e supersymmetry. We reformulate, in this new setting, the models of N=4 supersymmetric quantum mechanics associated with the off-shell multiplets (3, 4, 1) and (4, 4, 0). The latter admit a natural description as constrained superfields living in an analytic subspace of HR^{1+2|4}. We construct the relevant superfield actions consisting of a sigma-model as well as a superpotential parts and demonstrate that the superpotentials can be written off shell in a manifestly N=4 supersymmetric form only in the analytic superspace. The constraints implied by N=4 supersymmetry for the component bosonic target-space metrics, scalar potentials and background one-forms automatically follow from the harmonic superspace description. The analytic superspace is shown to be closed under the most general N=4, d=1 superconformal group D(2,1;\alpha). We give its action on the analytic superfields comprising the (3, 4, 1) and (4, 4, 0) multiplets, reveal a surprising relation between the latter and present the corresponding superconformally invariant actions. The harmonic superspace approach suggests a natural generalization of these multiplets, with a [2(n+1), 4n, 2(n-1)] off-shell content for n>2.