Commuting Clifford actions

TL;DR

The paper demonstrates that commuting Clifford algebra actions induce spinor representations of orthogonal Lie algebras, with applications to physics models like the standard model and Pati-Salam, through spectral triples.

Contribution

It introduces a method to derive spinor representations from commuting Clifford actions and constructs spectral triples for physical models.

Findings

Quadratic monomials from Clifford generators define orthogonal Lie algebra representations.

Construction of spectral triples for the Pati-Salam model with Spin(10) action.

Applications to high energy physics and unification theories.

Abstract

It shown that if a vector space carries commuting actions of two Clifford algebras, then the quadratic monomials using generators from either Clifford algebra determine a spinor representation of an orthogonal Lie algebra. Examples of this construction have applications to high energy physics, particularly to the standard model and unification. It is shown how to use Clifford data to construct spectral triples for the Pati-Salam model that admit an action of Spin(10).