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

TL;DR

This paper develops a boundary coupling framework for Lie algebroid Poisson sigma models using the BV formalism, proposing a BRST-invariant approach for representations up to homotopy, with implications for topological D-branes.

Contribution

It introduces a novel boundary coupling method for Lie algebroid Poisson sigma models utilizing the BV formalism, extending to representations up to homotopy and conjecturing a description of topological D-branes.

Findings

Proposes a general boundary coupling for Lie algebroid Poisson sigma models.

Uses BV formalism to ensure BRST invariance in the coupling.

Suggests a unified description of topological D-branes including A- and B-branes.

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.