Hierarchy of N=8 Mechanics Models

TL;DR

This paper constructs and analyzes a hierarchy of N=8 supersymmetric mechanics models using N=4 superspace, revealing a universal structure, conformally flat geometries, and new R-symmetric superfield Lagrangians.

Contribution

It introduces a hierarchical framework for N=8 supersymmetric mechanics models, deriving generic actions and revealing universal geometric and symmetry properties.

Findings

Derived the off-shell action for the (8,8,0) multiplet.

Showed all other multiplet actions follow via automorphic dualities.

Identified conformally flat target geometries with a scalar potential.

Abstract

Using the N=4 superspace approach in one dimension (time), we construct general N=8 supersymmetric mechanics actions for the multiplets (b,8,8-b) classified in hep-th/0406015, with the main focus on the previously unexplored cases of (8,8,0), (7,8,1) and (6,8,2), as well as on (5,8,3) for completeness. N=8 supersymmetry of the action amounts to a harmonicity condition for the Lagrangian with respect to its superfield arguments. We derive the generic off-shell component action for the ``root'' multiplet (8,8,0), prove that the actions for all other multiplets follow from it through automorphic dualities and argue that this hierarchical structure is universal. The bosonic target geometry in all cases is conformally flat, with a unique scalar potential (except for the root multiplet). We show that the N=4 superfield constraints respect the full R-symmetry and find the explicit realization of its quotient over the manifest R-symmetry on superfields and component fields. Several R-symmetric N=4 superfield Lagrangians with N=8 supersymmetry are either newly found or reproduced by a simple universal method.