Pure and Applied Mathematics Quarterly

Volume 9 (2013)

Number 1

Special Issue: In Honor of Dennis Sullivan, Part 1 of 2

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

Pages: 73 – 165

DOI: http://dx.doi.org/10.4310/PAMQ.2013.v9.n1.a3

Author

Kevin Costello (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

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 $\mathbb{P}^1$ of twisted supersymmetric gauge theories.

Keywords

supersymmetry, derived algebraic geometry, quantum field theory, deformation theory

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