Poisson Q-supermanifolds and differential Poisson sigma-models

Abstract We perform a systematic construction of supersymmetric Poisson sigma-models with an additional global supersymmetry in the geometric approach of Poisson Q-supermanifolds. Our analysis unifies Jackiw-Teitelboim supergravity and differential Poisson sigma-models exhibiting de Rham supersymmetry and reveals the existence of new models in the same family, such as a model with Lichnerowicz–Poisson supersymmetry, one based on a symmetric bilinear form and a class of models with super-Poisson structure of inhomogeneous degree. We emphasize the relation of the coadjoint representation of Lie algebroids to the global supersymmetry of these sigma-models.