Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

TL;DR

This paper explores the symmetries and representations of the ultra-multiplet, a minimal N=8 supersymmetry supermultiplet, revealing a common Spin(4) x Z(2) symmetry and constructing related Lagrangians.

Contribution

It catalogs effective symmetries of the ultra-multiplet family, establishes superfield representations for all adinkraic supermultiplets, and links them to E(8) structures.

Findings

Identified a common Spin(4) x Z(2) symmetry subgroup.

Constructed superfield representations for all adinkraic supermultiplets.

Developed quadratic Lagrangians with flux coupling.

Abstract

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.