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

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.

20 pages, 5 figures. Two references added

References in corpus (9)

• Refining the classification of the irreps of the 1D N-Extended Supersymmetry
• The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4 Mechanics
• Decomposition and Oxidation of the N-Extended Supersymmetric Quantum Mechanics Multiplets
• On non-minimal N=4 supermultiplets in 1D and their associated sigma-models
• The Real Anatomy of Complex Linear Superfields
• Adinkras for Clifford Algebras, and Worldline Supermultiplets
• Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics
• One-dimensional sigma-models with N=5,6,7,8 off-shell supersymmetries
• On Chiral and Nonchiral 1D Supermultiplets