I will talk about how nonlinear AKSZ sigma models behave in the BV-BFV formalism as a quantum gauge theory on manifolds possibly with boundary. I will present our recent result, which shows that a globalized version of the modified quantum master equation (mQME), which we call the modified differential quantum master equation (mdQME), holds and that the corresponding Grothendieck connection is flat. I will also talk about the example of the Poisson sigma model and explain how the Feynman diagrams lead to curvature terms, which spoil the mdQME, and how we can get rid of them. Finally, I will discuss some applications to the connection of gluing properties and deformation quantization. This is joint work with Alberto Cattaneo and Konstantin Wernli.
Fabien Vignes-Tourneret