Gauged sigma models and graded geometry

We study some graded geometric constructions appearing naturally in the context of gauge theories. In terms of Q-bundles we describe the gauge transformations of the (twisted) Poisson and Dirac sigma models. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds. This permits to obtain the mentioned sigma models by gauging essentially infinite dimensional groups and describe their symmetries in terms of classical differential geometry. This approach can also be useful to study supersymmetric gauge theories.