2025/03/13 by Shane Farnsworth, Farnsworth, Shane · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2503.10744
openalex publication_date 2025/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We solve an open problem in spectral geometry: the construction of finite-dimensional, discrete geometries coordinatized by non-simple, exceptional Jordan algebras. The approach taken is readily generalisable to broad classes of nonassociative geometries, opening the door to the spectral geometric desciption of gauge theories with exceptional symmetries. We showcase a proof-of-principle 2-point geometry corresponding to the internal space of an F4 × F4 gauge theory with scalar content restricted by novel conditions arising from the associative properties of the coordinate algebra. We then formally establish a setting for generalising to n-point exceptional Jordan geometries with distinct points coupled together via an action on 1-forms constructed as split Jordan bimodules.