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

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

2012-04-24

arxiv.org/abs/1204.5506v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, 5 figures

Scientific paper

"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 have been previously introduced and discussed. They include, among others, the notion of field content, connectivity symbol, commuting group, node choice group and so on.

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