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Non-associative gauge theory and higher spin interactions

Paul de Medeiros1 and Sanjaye Ramgoolam2

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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.

Keywords

Space-Time Symmetries

M(atrix) Theories

Non-Commutative Geometry

 

E-print Number: hep-th/0412027

Cited: by |

Refers: to

PACS

11.15.-q Gauge field theories

11.25.Yb M theory

11.10.Nx Noncommutative field theory

02.40.Gh Noncommutative geometry

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 03 (March 2005)

Received 14 December 2004, accepted for publication 26 March 2005

Published 22 April 2005



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