Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

Abstract

The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in $n$ dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in $n$ dimensions induce the structures of Batalin-Vilkovisky algebras on the target space.

25 pages

References in corpus (3)

• Deformation of BF theories, Topological Open Membrane and A Generalization of The Star Deformation
• Note on two-dimensional nonlinear gauge theories
• First order gauge field theories from a superfield formulation

Cited by in corpus (10)

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• The BV Formalization of Chern-Simons Theory on Deformed Superspace
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• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach
• Self-interactions in a topological BF-type model in D=5
• Dimensional Reduction of Nonlinear Gauge Theories
• Topological A-Type Models with Flux
• On the generalized Freedman-Townsend model