Adinkras, 0-branes, holoraumy and the SUSY QFT/QM correspondence

Abstract

We propose the recently defined "Holoraumy Tensor" to play a critical role in defining a metric to establish a correspondence between 4D, [Formula: see text]-extended 0-brane-based valise supermultiplet representations and, correspondingly via "SUSY Holography," on the space of 1D, N-extended network-based adinkras. Using an analogy with the su(3) algebra, it is argued the 0-brane holoraumy tensors play the role of the " d -coefficients" and provide a newly established tool for investigating supersymmetric representation theory.

Adinkras from ordered quartets of BC4 Coxeter group elements and regarding 1,358,954,496 matrix elements of the Gadget

“…These results support the concept of "SUSY holography" by showing the "angles" [38][39][40][41][42] between any two adinkras constructed from ordered quartets of BC 4 elements take on exactly and only the same values as the "angles" [40] between any of the 4D, N = 1 supermultiplets with minimal numbers of bosons and fermions. The presentation in section 3 is made in terms of a visual/graphical representation.…”

“…The fact that 14,155,776 -36,864 = 14,118,912 implies that among the 36,864 associated unit vectors many are colinear to one another. The angle arccos (−1/3) has been noted for some time in our past research papers [36][37][38][39][40]. In fact, with the exception of the angle of arccos (1/3) all the other angles have been found in our previous calculations.…”

“…In facing the problem of reconstructing 4D simple supermultiplets from adinkras, unlike the successful paths shown for the analogous problem in 2D, another path has been pursued also [36][37][38][39][40][41][42]. This alternate path is based on the fact that closed four-cycles for four color valise adinkras possess naturally an SO(4) symmetry.…”

“…We have given the name of "bosonic holoraumy matrices" and "fermionic holoraumy matrices," respectively, to the sets denoted by V IJ (R) and V IJ (R) [36][37][38][39][40] and defined via the equations…”

A proposal on culling & filtering a coxeter group for 4D, N $$ \mathcal{N} $$ = 1 spacetime SUSY representations: revised

“…Forming the absolute values of the entries in the L-matrices and R-matrices leads to the conventional definitions of adjacency matrices for bipartitte graphs. The commutator algebra of the L-matrices and R-matrices define the 'holoraumy' [6][7][8][9][10] associated with the graph. Since this class of adinkra graphs possess an obvious SO(4) symmetry, by exploiting the results in section 3, the spinorial nodes of these adinkra graphs can provide a realization upon which the SO(1, 3) Dirac γ-matrices can act.…”