Update on Supersymmetric Field Theory and Invariants of Smooth Four-Manifolds

I will give a lightning review of results on this subject from 1988-1998 and then describe more recent developments, mostly current work in progress.  First, I will describe topological twisting of Lagrangian N=2 d=4 field theories in terms of the general concept of reduction of structure group. Second, I will discuss a few results and issues related to partially twisted 5d super-Yang-Mills and the "K-theoretic Donaldson invariants." Finally, time permitting, I will discuss how one can construct analogs of Donaldson invariants for families of four-manifolds by coupling to a truncated version of superconformal gravity. The last topic appeared recently in collaboration with M. Rocek and V. Saxena as e-Print:2311.08394

Background papers for 1988--1998: 

1. E. Witten, ``Topological Quantum Field Theory,'' CMP 117 (1988) 353 

2. N. Seiberg and E. Witten, ``Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory,'' hep-th/9407087

3. E. Witten, ``Monopoles and four manifolds,'' hep-th/9411102 

4. G. Moore and E. Witten, ``Integration over the u plane in Donaldson theory,'' hep-th/9709193

An up-to-date review recently appeared: 

J. Manschot, ``Four-Manifold Invariants and Donaldson-Witten Theory,''  e-Print:2312.14709