Topological Quantum Field Theories from Compact Lie Groups

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Topological Quantum Field Theories from Compact Lie Groups

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Title: Topological Quantum Field Theories from Compact Lie Groups
Author: Freed, Daniel; Hopkins, Michael J.; Lurie, Jacob Alexander; Teleman, Constantin

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Citation: Freed, Daniel, Michael J. Hopkins, Jacob Alexander Lurie, and Constantin Teleman. 2010. Topological quantum field theories from compact lie groups. In A Celebration of the Mathematical Legacy of Raoul Bott, vol. 50 of CRM Proceedings and Lecture Notes, ed. P. Robert Kotiuga, 367-403. Providence, RI: American Mathematical Society.
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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.
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