Topological Quantum Field Theories from Compact Lie Groups

Details Topological Quantum Field Theories from Compact Lie Groups Topological Quantum Field Theories from Compact Lie Groups

2009-05-06

arxiv.org/abs/0905.0731v2

Mathematics

Algebraic Topology

39 pages, submission to proceedings of "A Celebration of the Mathematical Legacy of Raoul Bott"; v2 has minor changes

Scientific paper

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.

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