Letters in Mathematical Physics

, Volume 102, Issue 1, pp 31–64 | Cite as

Boundary Coupling of Lie Algebroid Poisson Sigma Models and Representations up to Homotopy



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.

Mathematics Subject Classification (2000)

Primary 81T45 Secondary 81T70 81T30 


topological field theories Poisson sigma models Lie algebroids Batalin–Vilkovisky formalism D-branes 


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Copyright information

© Springer 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK

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