Nonlinear (4, 8, 4) Multiplet of N=8, d=1 Supersymmetry

TL;DR

This paper develops a nonlinear off-shell N=8, d=1 supersymmetric multiplet using harmonic superspace, revealing new geometric structures and potential deformations of the four-sphere metric.

Contribution

It introduces a novel nonlinear (4,8,4) multiplet in N=8, d=1 supersymmetry via harmonic superspace, expanding the understanding of superconformal symmetry breaking and target space geometry.

Findings

Constructed the nonlinear multiplet q^{1,1} with covariant harmonic constraints.

Derived the general form of superconformal actions and target space metrics.

Identified the target metric as a conformally flat deformation of S^4.

Abstract

We construct a nonlinear version of the d=1 off-shell N=8 multiplet (4,8,4), proceeding from a nonlinear realization of the superconformal group OSp(4*|4) in the N=8, d=1 analytic bi-harmonic superspace. The new multiplet is described by a double-charged analytic superfield q^{1,1} subjected to some nonlinear harmonic constraints which are covariant under the OSp(4*|4) transformations. Together with the analytic superspace coordinates, q^{1,1} parametrizes an analytic coset manifold of OSp(4*|4) and so is a Goldstone superfield. In any q^{1,1} action the superconformal symmetry is broken, while N=8, d=1 Poincar\'e supersymmetry can still be preserved. We construct the most general class of such supersymmetric actions and find the general expression for the bosonic target metric in terms of the original analytic Lagrangian superfield density which is thus the target geometry prepotential. It also completely specifies the scalar potential. The metric is conformally flat and, in the SO(4) invariant case, is a deformation of the metric of a four-sphere S^4.