Adinkras, Dessins, Origami, and Supersymmetry Spectral Triples

TL;DR

This paper explores the spectral geometry of 1D Supersymmetry Algebras using Adinkra graphs, dessins d'enfant, and origami curves, and computes spectral action functionals via the Selberg trace formula.

Contribution

It introduces a novel geometric framework linking supersymmetry algebras with combinatorial and algebraic curves, and computes associated spectral actions.

Findings

Spectral action functionals expressed through Selberg trace formula

Classification of supersymmetry algebras via Adinkra graphs and dessins

Connection between supersymmetry and algebraic curves

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.