Lie Algebroid Yang Mills with Matter Fields

Abstract

Lie algebroid Yang-Mills theories are a generalization of Yang-Mills gauge theories, replacing the structural Lie algebra by a Lie algebroid E. In this note we relax the conditions on the fiber metric of E for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie algebroid connection. The presentation is kept in part explicit so as to be accessible also to a less mathematically oriented audience.

24 pages, accepted for publication in J. Geom. Phys

References in corpus (8)

• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• Lectures on Integrability of Lie Brackets
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• Algebroid Yang-Mills Theories
• Gravity from Lie algebroid morphisms
• Characteristic classes associated to Q-bundles
• Lie algebroids, Lie groupoids and TFT

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