Non-associative gauge theory and higher spin interactions

TL;DR

This paper develops a framework for gauge theories on non-associative fuzzy spaces, revealing connections to higher spin fields and extending traditional Yang-Mills theory to a non-associative context.

Contribution

It introduces a novel gauge theory formulation on non-associative fuzzy spaces, linking higher spin interactions with non-commutative geometry and extending Yang-Mills theory.

Findings

Describes gauge theory on non-associative fuzzy spaces.

Shows higher spin fields emerge naturally in this framework.

Connects the theory to non-commutative Yang-Mills in the associative limit.

Abstract

We give a framework to describe gauge theory on a certain class of commutative but non-associative fuzzy spaces. Our description is in terms of an Abelian gauge connection valued in the algebra of functions on the cotangent bundle of the fuzzy space. The structure of such a gauge theory has many formal similarities with that of Yang-Mills theory. The components of the gauge connection are functions on the fuzzy space which transform in higher spin representations of the Lorentz group. In component form, the gauge theory describes an interacting theory of higher spin fields, which remains non-trivial in the limit where the fuzzy space becomes associative. In this limit, the theory can be viewed as a projection of an ordinary non-commutative Yang-Mills theory. We describe the embedding of Maxwell theory in this extended framework which follows the standard unfolding procedure for higher spin gauge theories.