N=8 Mechanics in SU(2)xSU(2) Harmonic Superspace

TL;DR

This paper develops an ${ m N}=8$ supersymmetric mechanics framework using harmonic superspace, constructing superfield actions, analyzing symmetry transformations, and formulating supergravity with off-shell multiplets.

Contribution

It introduces a novel ${ m N}=8$ harmonic superspace approach for supersymmetric mechanics, including new superfield actions and supergravity formulations with off-shell multiplets.

Findings

Constructed general superfield and component actions for ${ m N}=8$ multiplets.

Identified the symmetry algebra as an ${ m N}=8$ extension of the Heisenberg algebra with a central charge.

Presented the first off-shell ${ m N}=8$ supergravity action with local supersymmetry.

Abstract

The ${\cal N}{=}8, 1D$ analytic bi-harmonic superspace is shown to provide a natural setting for ${\cal N}{=}8$ supersymmetric mechanics associated with the off-shell multiplet ${\bf (4, 8, 4)}$ . The latter is described by an analytic superfield $q^{1,1}$, and we construct the general superfield and component actions for any number of such multiplets. The set of transformations preserving the flat superspace constraints on $q^{1,1}$ constitutes ${\cal N}{=}8$ extension of the two-dimensional Heisenberg algebra {\bf h}(2), with an operator central charge. The corresponding invariant $q^{1,1}$ action is constructed. It is unique and breaks 1D scale invariance. We also find a one-parameter family of scale-invariant $q^{1,1}$ actions which, however, are not invariant under the full ${\cal N}{=}8$ Heisenberg supergroup. Based on preserving the bi-harmonic Grassmann analyticity, we formulate ${\cal N}{=}8, 1D$ supergravity in terms of the appropriate analytic supervielbeins. For its truncated version we construct, both at the superfield and component levels, the first example of off-shell $q^{1,1}$ action with local ${\cal N}{=}8, 1D$ supersymmetry. This construction can be generalized to any number of self-interacting $q^{1,1}$ .