Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models

TL;DR

This paper classifies pure and entangled N=4 supermultiplets in one-dimensional supersymmetry, introduces an explicit entangled supermultiplet example, and constructs associated sigma-models, expanding understanding of supermultiplet structures.

Contribution

It provides the first explicit example of an entangled N=4 supermultiplet that cannot be represented graphically, and develops a classification framework for pure and entangled supermultiplets.

Findings

Existence of entangled supermultiplets without graphical representation

Construction of a sigma-model based on an entangled supermultiplet

Distinction between supermultiplet equivalence and graph equivalence

Abstract

"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs are known as "Adinkras"). We further prove the existence of "entangled" linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3,8,5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as chirality and coloring can discriminate different supermultiplets. The tools used in our classification include, among others, the notion of field content, connectivity symbol, commuting group, node choice group and so on.