On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

Details On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

2005-12-06

arxiv.org/abs/math-ph/0512016v2

Int.J.Mod.Phys.A22:869-930,2007

Physics

Mathematical Physics

LaTeX, 58 pages, 52 illustrations in color; minor typos corrected

Scientific paper

10.1142/S0217751X07035112

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.

Affiliated with

Also associated with

No associations

Rating

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-428851