Adinkras, dessins, origami, and supersymmetry spectral triples. (English) Zbl 1445.17002
The authors investigate the spectral geometry and spectral action functionals associated to 1D supersymmetry algebras, using the classification of these superalgebras in terms of Adinkra graphs, a class of decorated \(N\)-regular, \(N\)-edge colored bipartite graphs related to representations of the \(N\)-extended one-dimensional super Poincaré algebra (see [C. Doran et al., Adv. Theor. Math. Phys. 19, No. 5, 1043–1113 (2015; Zbl 1382.14009)]). Other closely related constructions are dessins d’enfant and origami curves. The resulting spectral action functionals are computed in terms of the Selberg (super) trace formula and the Poisson summation formula.
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:
| 17A70 | Superalgebras |
| 05C15 | Coloring of graphs and hypergraphs |
| 14H57 | Dessins d’enfants theory |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 30F99 | Riemann surfaces |
| 81T60 | Supersymmetric field theories in quantum mechanics |
Keywords:
Adinkra graph; 1D supersymmetry algebras; dessins d’enfant; origami; spectral action; Selberg supertrace formula; bipartite graphs; super Poincaré algebraCitations:
Zbl 1382.14009Software:
AdinkrasReferences:
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