Biharmonic Superspace for N=4 Mechanics

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 Poincaré 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;α). 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. PACS: 11.30.Pb, 11.15.-q, 11.10.Kk, 03.65.-w