Perturbative calculations in Chern-Simons with conformal boundary conditions
I will review a bit of perturbative Chern-Simons theory (a topological field theory giving invariants of knots and of 3-manifolds) and then show what to do if we have a non-topological boundary condition given by a generalized metric. This boundary condition is quite natural - it generalizes the famous chiral boundary condition (from CS/WZW correspondence). On the classical level it requires a complex structure on the boundary, but quantization may require enhancing the conformal structure to a Riemannian metric. If everything goes smoothly, we'll see what happens with 1-loop Feynman diagrams and find the so-called generalized Ricci tensor there, giving the renormalization group flow of the generalized metric. If things go inexplicably well, I'll also say something about the Courant model, of which Chern-Simons is a special case.