The Lie algebroid Poisson sigma model

The Poisson--Weil sigma model, worked out by us recently, stems from gauging a Hamiltonian Lie group symmetry of the target space of the Poisson sigma model. Upon gauge fixing of the BV master action, it yields interesting topological field theories such as the 2--dimensional Donaldson-Witten topological gauge theory and the gauged A topological sigma model. In this paper, generalizing the above construction, we construct the Lie algebroid Poisson sigma model. This is yielded by gauging a Hamiltonian Lie groupoid symmetry of the Poisson sigma model target space. We use the BV quantization approach in the AKSZ geometrical version to ensure consistent quantization and target space covariance. The model has an extremely rich geometry and an intricate BV cohomology, which are studied in detail.