The superfield realization conjecture for engineerable Adinkra topologies

An Adinkra is a colored graph encoding a one-dimensional supersymmetry representation, and its topology records the graph structure up to the relevant identifications. A topology is engineerable if it occurs for an Adinkra compatible with the engineering-dimension assignments of the component fields. For each positive integer NN, consider the topologies of engineerable Adinkras for NN-extended supersymmetry.

Superfield realization conjecture. For every NN and every topology of engineerable Adinkras, there exists a corresponding set of superderivative constraints such that the set of superfields satisfying these constraints has an Adinkra of that topology.

The claim would establish the existence of a superfield realization for every engineerable Adinkra topology. The source presents this as an assumption whose affirmation is tempting but notes that the required algorithm for generating all two-to-one identifications of higher-NN cubical Adinkras, together with the corresponding superfield constraints, had not yet been constructed.

Sources & referencesView supporting material

Primary source

C. F. Doran, M. G. Faux, S. J. Gates,, T. Hubsch, K. M. Iga and G. D. Landweber, “On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields”, arXiv:math-ph/0512016 (2006).

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