The Batalin-Vilkovisky formalism for field theory and general covariance

AKSZ field theories are a class of field theories generalizing the Chern-Simons model. They exhibit general covariance under diffeomorphisms of spacetime. In this talk, I will recast general covariance as a Maurer-Cartan equation for a certain curved differential graded Lie algebra. In joint work with Sean Pohorence, I have shown that the superparticle, a toy model of the (Green-Schwarz) superstring, while not an AKSZ model, does exhibit general covariance in the sense that the curved Maurer-Cartan equation mentioned above may be solved. The proof requires the use of the Thom-Whitney normalization of curved differential graded Lie algebras, introduced by Sullivan in his work on rational homotopy theory