(Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints

Abstract

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand.

24 pages

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Cited by in corpus (7)

• Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory
• Super Cartan geometry and the super Ashtekar connection
• Yang-Mills gravity in biconformal space
• Higher Chern-Simons based on (2-)crossed modules
• Generalized forms and gravitation
• Generalized forms, vector fields and superspace
• Generalized Chern-Simons action principles for gravity