Topological Quantum Field Theories from Compact Lie Groups
Abstract
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also develop from different points of view an associated 4-dimensional invertible topological field theory which encodes the anomaly of Chern-Simons. Finite gauge groups are also revisited, and we describe a theory of "finite path integrals" as a general construction for a certain class of finite topological field theories. Topological pure gauge theories in lower dimension are presented as a warm-up.
Cite
@article{arxiv.0905.0731,
title = {Topological Quantum Field Theories from Compact Lie Groups},
author = {Daniel S. Freed and Michael J. Hopkins and Jacob Lurie and Constantin Teleman},
journal= {arXiv preprint arXiv:0905.0731},
year = {2009}
}
Comments
39 pages, submission to proceedings of "A Celebration of the Mathematical Legacy of Raoul Bott"; v2 has minor changes