Biharmonic Superspace for N=4 Mechanics

TL;DR

This paper introduces a biharmonic superspace framework for N=4 supersymmetric mechanics, enabling a unified treatment of supermultiplets and their mirror counterparts, with applications to constructing models with specific target manifolds.

Contribution

It develops a novel biharmonic superspace approach for N=4 mechanics, allowing symmetric handling of supermultiplets and their mirrors, and demonstrates its use in constructing a new mechanics model.

Findings

Biharmonic superspace extends N=4 superspace with dual harmonic variables.

It describes supermultiplets and superconformal properties uniformly.

A new N=4 mechanics model with a seven-dimensional target manifold is constructed.

Abstract

We develop a new superfield approach to N=4 supersymmetric mechanics based on the concept of biharmonic superspace (bi-HSS). It is an extension of the N=4,d=1 superspace by two sets of harmonic variables associated with the two SU(2) factors of the R-symmetry group SO(4) of the N=4, d=1 super Poincar\'e algebra. There are three analytic subspaces in it: two of the Grassmann dimension 2 and one of the dimension 3. They are closed under the infinite-dimensional "large" N=4 superconformal group, as well as under the finite-dimensional superconformal group D(2,1;\alpha). The main advantage of the bi-HSS approach is that it gives an opportunity to treat N=4 supermultiplets with finite numbers of off-shell components on equal footing with their ``mirror'' counterparts. We show how such multiplets and their superconformal properties are described in this approach. We also define nonpropagating gauge multiplets which can be used to gauge various isometries of the bi-HSS actions. We present an example of nontrivial N=4 mechanics model with a seven-dimensional target manifold obtained by gauging an U(1) isometry in a sum of the free actions of the multiplet (4,4,0) and its mirror counterpart.