New Model of N=8 Superconformal Mechanics

TL;DR

This paper constructs an N=8 superconformal mechanics model using superfield methods, revealing a new invariant action under the exceptional F(4) superconformal group with potential terms that break some symmetries.

Contribution

It introduces a novel N=8 superconformal action for the (1,8,7) multiplet using a superfield approach, expanding the understanding of superconformal mechanics.

Findings

Constructed an N=8 superconformal action invariant under F(4)

Demonstrated the general N=8 action as a sum of superconformal and free parts

Identified Fayet-Iliopoulos terms generating scalar potentials that break some symmetries

Abstract

Using an N=4, d=1 superfield approach, we construct an N=8 supersymmetric action of the self-interacting off-shell N=8 multiplet {\bf (1, 8, 7)}. This action is found to be invariant under the exceptional N=8, d=1 superconformal group F(4) with the R-symmetry subgroup SO(7). The general N=8 supersymmetric {\bf (1, 8, 7)} action is a sum of the superconformal action and the previously known free bilinear action. We show that the general action is also superconformal, but with respect to redefined superfield transformation laws. The scalar potential can be generated by two Fayet-Iliopoulos N=4 superfield terms which preserve N=8 supersymmetry but break the superconformal and SO(7) symmetries.