AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

Abstract

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.

13 pages, based on lectures at Rencontres mathematiques de Glanon 2003

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• Transitive Courant algebroids and double symplectic groupoids
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• From BFV to BV and spacetime covariance
• Super AKSZ construction, integral forms, and the 2-dimensional $\mathcal{N}=(1,1)$ sigma model
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• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• BV Quantization
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• Higher Courant-Dorfman algebras and associated higher Poisson vertex algebras
• The standard cohomology of regular Courant algebroids
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• Categorification of VB-Lie algebroids and VB-Courant algebroids
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