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

Abstract

A Gadget, more precisely a scalar Gadget, is defined as a mathematical calculation acting over a domain of one or more adinkra graphs and whose range is a real number. A 2010 work on the subject of automorphisms of adinkra graphs, implied the existence of multiple numbers of Gadgets depending on the number of colors under consideration. For four colors, this number is two. In this work, we verify the existence of a second such Gadget and calculate (both analytically and via explicit computer-enabled algorithms) its 1,358,954,496 matrix elements over 36,864 minimal valise adinkras related to the Coxeter Group BC 4 .

4D, N = 1 Matter Gravitino Genomics

“…This analysis is already being done and we hope to complete it soon. In addition, it would be interesting to see what other gadgets, such as those described in [27,35], encode for the 12 × 12, 20 × 20, and higher spin multiplets. In future works, with the 12 × 12 and higher spin multiplets, we look for more data to use with the 20 × 20 gadget data presented in this work to fix a canonical nodal field definition convention that remains consistent among all multiplets and perhaps to fix the diagonal Lagrangian parameters that will continue to be present in higher spin multiplets.…”

“…Dimensional enhancement, or SUSY holography, is the effort to build higher dimensional SUSY representations from lower dimensional representations [14][15][16]. To aid in sorting out which of the multitude of lower dimensional systems are candidates for dimensional enhancement, a tool known as holoraumy is being developed [17][18][19][20][21][22][23][24][25][26][27]. On the 0-brane with N SUSY transformations D I , holoraumy is defined as the commutator of two supersymmetric transformations D I acting on the bosons Φ or fermions Ψ of a particular representation…”

“…In a sense, this paper is a sister paper of the recent work [26]: this paper reviews the status of SUSY genomics, focusing on 4D dynamics, whereas [26] reviews the status of SUSY holography, focusing on 1D dynamics. It is the view of at least one of the authors of this paper (KS) that building a complete picture of SUSY holography [14][15][16] would require efforts into SUSY genomics [1][2][3], enumeration techniques [34,35], and classification schemes [17][18][19][20][21][22][23][24][25][26][27]. The main results of the paper are as follows:…”

4D, $\mathcal{N}=1$ Matter Gravitino Genomics

“…of lower dimensional systems are candidates for dimensional enhancement, a tool known as holoraumy is being developed [17,18,19,20,21,22,23,24,25,26,27]. On the 0-brane with N SUSY transformations D I , holoraumy is defined as the commutator of two supersymmetric transformations D I acting on the bosons Φ or fermions Ψ of a particular representation…”

“…In a sense, this paper is a sister paper of the recent work [26]: this paper reviews the status of SUSY genomics, focusing on 4D dynamics, whereas [26] reviews the status of SUSY holography, focusing on 1D dynamics. It is the view of at least one of the authors of this paper (KS) that building a complete picture of SUSY holography [14,15,16] would require efforts into SUSY genomics [1,2,3], enumeration techniques [34,35], and classification schemes [17,18,19,20,21,22,23,24,25,26,27]. The main results of the paper are as follows:…”