N = 4 supersymmetric mechanics in harmonic superspace

Abstract

We define N = 4, d = 1 harmonic superspace HR1+2|4 with an SU(2)/U(1) harmonic part, SU(2) being one of two factors of the R-symmetry group SU(2) × SU(2) of N = 4, d = 1 Poincaré 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 HR1+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 superconformai group D(2, 1; α). We give its action on the analytic superflelds 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. © SISSA/ISAS 2003.