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. 
Alexander Quintero Velez
math-ph hep-th math.AG math.DG math.MP