Adinkras for Mathematicians

Adinkras and SUSY holography: Some explicit examples

“…the discovery that adinkras (and therefore off-shell supersymmetry representation theory) describe spaces of 'marked cubical topology' [5], (b.) the irreducible representations of adinkras are determined by self-dual block linear error-correcting codes [6], and (c.) that there exist a relation to mathematical structures called posets [7]. The L-matrices have a well defined role for one dimensional quantum mechanical systems.…”

4D, N = 1 Supersymmetry Genomics (II)

“…In a sense the field theory problems have been mapped (we believe with complete fidelity) into a realm of graph theory, coding theory, and other mathematical formalism that permit a rigorous study of all such problems. In fact, recently there has been proposed a highly formalized mathematical framework [11] that may allow the investigation (and hopefully resolution) of long unsolved problems in this field.…”

Graph theory and qubit information systems of extremal black branes

“…Henceforth, we refer to them as bosonic graphs. The Adinkras have been introduced in the study of supersymmetric representation theory [32,33,[37][38][39][40][41]. In the usual diagram representation, Adinkras are formed by nodes and lines.…”

“…In this paper, we reconsider the study of the extremal black branes in the framework of quantum information using graph theory based on the so-called Adinkras [32,33]. More precisely, we establish a one-to-one correspondence between qubit systems, Adinkras and extremal black branes embedded in maximally supersymmetric supergravity obtained from a low energy limit of a type IIA superstring compactified on T n .…”