Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4
arXiv:1111.4234
Abstract
These notes explore some aspects of formal derived geometry related to classical field theory. One goal is to explain how many important classical field theories in physics -- such as supersymmetric gauge theories and supersymmetric sigma-models -- can be described very cleanly using derived geometry. In particular, I describe a mathematically natural construction of Kapustin-Witten's P^1 of twisted supersymmetric gauge theories.
Dedicated to Dennis Sullivan on the occassion of his 70th birthday. Version 2: many typos corrected. Version 3: some further corrections and clarifications, no significant changes