Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples

Abstract

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 origami curves. The resulting spectral action functionals are computed in terms of the Selberg (super) trace formula.

Quantum Statistical Mechanics of the Absolute Galois Group

“…A product operation on dessins induced by the fibered product of the Belyi maps was discussed in [58]. Let D 1 and D 2 be two dessins with f i : X i → P 1 (C) the associated Belyi maps.…”

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

“…Our study of "Garden Algebras" [1,2] and "adinkras" [3] has opened multiple pathways for understanding the relation of supersymmetry, in most unexpected ways, to topics in mathematics. Such a demonstration appeared in the recent examples [4,5] connecting adinkras to algebraic geometry as the latest following a host of others [6,7,8,9,10,11,12,13].…”