Boundary coupling of Lie algebroid Poisson sigma models and representations up to homotopy

Abstract

A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin-Vilkovisky formalism in the AKSZ geometrical version, to write a BRST-invariant coupling for a representation up to homotopy of the target Lie algebroid or its subalgebroids. These considerations lead to a conjectural description of topological D-branes on generalized complex manifolds, which includes A-branes and B-branes as special cases.

24 pages, no figures; v2: published version

References in corpus (7)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Localization and traces in open-closed topological Landau-Ginzburg models
• Poisson sigma model on the sphere
• Lie algebroids, Lie groupoids and TFT
• Poisson reduction and branes in Poisson-Sigma models
• Anomalies and Graded Coisotropic Branes
• The Lie algebroid Poisson sigma model

Cited by in corpus (1)

• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons