Non-associative gauge theory and higher spin interactions

Details Non-associative gauge theory and higher spin interactions Non-associative gauge theory and higher spin interactions

2004-12-02

arxiv.org/abs/hep-th/0412027v2

JHEP 0503 (2005) 072

Physics

High Energy Physics

High Energy Physics - Theory

1+49 pages, LaTeX; references and clarifying remarks added

Scientific paper

10.1088/1126-6708/2005/03/072

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.

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