Related papers: A combinatorial introduction to Adinkras
The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras as part of a larger effort we call supersymmetry `genomics.' Recent…
Adinkras are graphs that encode a supersymmetric representation's transformation laws that have been reduced to one dimension, that of time. A goal of the supersymmetry ``genomics'' project is to classify all 4D, $\mathcal{N}=1$ off-shell…
The problem of classifying off-shell representations of the $N$ -extended one-dimensional super Poincar\'e algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as Adinkras. In…
Starting from higher dimensional adinkras constructed with nodes referenced by Dynkin Labels, we define "adynkras." These suggest a computationally direct way to describe the component fields contained within supermultiplets in all…
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…
An adinkra is a graph-theoretic representation of spacetime supersymmetry. Minimal four-color valise adinkras have been extensively studied due to their relations to minimal 4D, $\cal N$ = 1 supermultiplets. Valise adinkras, although an…
The problem of classifying off-shell representations of the $N$-extended one-dimensional super Poincar\'{e} algebra is closely related to the study of a class of decorated $N$-regular, $N$-edge colored bipartite graphs known as {\em…
We present further progress toward a complete classification scheme for describing supermultiplets of N-extended worldline supersymmetry, which relies on graph-theoretic topological invariants. In particular, we demonstrate a relationship…
Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for…
"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs…
The nilpotence variety for extended supersymmetric quantum mechanics is a cone over a quadric in projective space. The pure spinor correspondence, which relates the description of off-shell supermultiplets to the classification of modules…
We investigate the spectral geometry and spectral action functionals associated to 1D Supersymmetry Algebras, using the classification of these superalgebras in terms of Adinkra graphs and the construction of associated dessin d'enfant and…
Adinkras are graphical representations of the gauge invariant field components in supersymmetric theories and their orbits under the action of supersymmetry (SUSY) generators in the context of supermultiplets. A discussion is given that…
Motivated by the search for embedded on-shell supermultiplets in higher dimensional off-shell theories, we investigate several 16-color supermultiplets and their topology. An Adinkra's topology is known to be equivalent to…
We develop a new approach to deal with qubit information systems using toric geometry and its relation to Adinkra graph theory. More precisely, we link three different subjects namely toric geometry, Adinkras and quantum information theory.…
There are many different algebraic, geometric and combinatorial objects that one can attach to a complex polynomial with distinct roots. In this article we introduce a new object that encodes many of the existing objects that have…
For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented.…
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
Every finite-dimensional unitary representation of the N-extended worldline supersymmetry without central charges may be obtained by a sequence of differential transformations from a direct sum of minimal Adinkras, simple supermultiplets…
With this work we aim to show how Mathematica can be a useful tool to investigate properties of combinatorial structures. Specifically, we will face enumeration problems on independent subsets of powers of paths and cycles, trying to…