Spacetime Spin and Chirality Operators for Minimal 4D, $\cal N$ = 1 Supermultiplets From BC${}_4$ Adinkra-Tessellation of Riemann Surfaces

Gates, S. James

doi:10.48550/arxiv.1701.08102

Cited by 1 publication

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“…From this procedure, although we have a large number of different 1D, N = 4 adinkras, they all collapse into the same 4D, N = 1 version. It is useful to also recall that the aggregation of nodes leads to "dimensional enhancement" [34,35,36] that allows the adinkra nodes to carry representations of the four dimensional Lorentz group. It is useful to know one of the nodes at the lowest level of the bottom right graph in Figure 3.3 (i.e.…”

Section: Graph Theory Perspective: Adinkramentioning

confidence: 99%

Superfield Component Decompositions and the Scan for Prepotential Supermultiplets in 10D Superspaces

Gates,

Hu,

Mak

2019

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The first complete and explicit SO(1,9) Lorentz descriptions of all component fields contained in the N = 1, N = 2A, and N = 2B unconstrained scalar 10D superfields are presented. These are made possible by a discovery of the dependence of the superfield component expansion on the branching rules of irreducible representations in one ordinary Lie algebra into one of its Lie subalgebras. Adinkra graphs for ten dimensional superspaces are defined for the first time, whose nodes depict spin bundle representations of SO(1,9). A consequential deliverable of this advance is it provides the first explicit, in terms of component fields, examples of all the off-shell 10D Nordström SG theories relevant to string theory, without off-shell central charges that are reducible but with finite numbers of fields. An analogue of Breitenlohner's approach is implemented to scan for superfields that contain graviton(s) and gravitino(s), which are the candidates for the superconformal prepotential superfields of 10D off-shell supergravity theories and Yang-Mills theories.

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Section: Graph Theory Perspective: Adinkramentioning

confidence: 99%