Topics In The Relation Of Four-Manifold Invariants And Supersymmetric Field Theory

We will begin with a review of topological twisting as a choice of background fields. We then review the standard paradigm for the formulation of Donaldson invariants as correlation functions in twisted supersymmetric N=2 d=4 quantum field theory, together with the quantum field theory (QFT) derivation of the relation of the Donaldson invariants to Seiberg-Witten invariants. We then consider what can be said using other twisted QFTs. We present some new results on the four-manifold invariants derived from N=2 supersymmetric QCD. We then move on to 5d theories and the “K-theoretic Donaldson invariants” and comment briefly on the 6d theories and the “elliptic Donaldson invariants.” In the unlikely event that time permits we finish with the extension to families of four-manifolds, where the coupling to a suitably twisted and truncated superconformal gravity is expected to produce invariants valued in the cohomology of the classifying space of the diffeomorphism group of the four-manifold.

Zoom link: https://harvard.zoom.us/j/97952922247?pwd=PMJqfJoalYI19S0z1RgDme2dNQeEiS.1
Password / Meeting ID: 868088 / 979 5292 2247