Discretized Yang-Mills and Born-Infeld actions on finite group geometries

Abstract

Discretized nonabelian gauge theories living on finite group spaces G are defined by means of a geometric action \int Tr F \wedge *F. This technique is extended to obtain discrete versions of the Born-Infeld action. The discretizations are in 1-1 correspondence with differential calculi on finite groups. A consistency condition for duality invariance of the discretized field equations is derived for discretized U(1) actions S[F] living on a 4-dimensional abelian G. Discretized electromagnetism satisfies this condition and therefore admits duality rotations. Yang-Mills and Born-Infeld theories are also considered on product spaces M^D x G, and we find the corresponding field theories on M^D after Kaluza-Klein reduction on the G discrete internal spaces. We examine in some detail the case G=Z_N, and discuss the limit N -> \infty. A self-contained review on the noncommutative differential geometry of finite groups is included.

31 pages, LaTeX. Improved definition of pairing between tensor products of left-invariant one-forms

References in corpus (2)

• Noncommutative Field Theory
• Duality Rotations and BPS Monopoles with Space and Time Noncommutativity

Cited by in corpus (6)

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• Differential Geometry of Group Lattices
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• Riemannian Geometry of Bicovariant Group Lattices
• Noncommutative de Rham cohomology of finite groups