We propose a new class of sigma models by gauging of AKSZ sigma models. Analysis is based on graded manifold structures called Q-manifolds. As a typical example, we discuss extensions of Poisson sigma models. By introducing additional gauge symmetries, associated to a Lie groupoid (Lie algebroid) on the target space, Poisson sigma models are extended to gauged sigma models of generalized AKSZ type. The consistency of the theory is ensured by geometric conditions on Lie algebroids such as curvatures and torsions. We also present analysis of models in the presence of boundaries. If we have time, gauging of the Courant sigma model is discussed.

The talk is based on arXiv:2309.10996 [math.DG] and 2604.23496 [math-ph].