Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4

Details Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4 Notes on supersymmetric and holomorphic field theories in dimensions 2 and 4

2011-11-17

arxiv.org/abs/1111.4234v2

Mathematics

Quantum Algebra

Dedicated to Dennis Sullivan on the occassion of his 70th birthday. Version 2: many typos corrected

Scientific paper

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.

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