An article that we wrote for a book on mathematical aspects of quantum field theory:
A higher stacky perspective on Chern-Simons theory
Damien Calaque et al. (eds.)
Mathematical Aspects of Quantum Field Theories
Mathematical Physics Studies, Springer 2014
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern-Simons theory is naturally localized (“extended”, “multi-tiered”) to a map on the universal moduli stack of principal connections, a map that itself modulates a circle-principal 3-connection on that moduli stack, and how the iterated transgressions of this extended Lagrangian unify the action functional with its prequantum bundle and with the WZW-functional. In the second part we provide a brief review and outlook of the higher prequantum field theory of which this is a first example. This includes a higher geometric description of supersymmetric Chern-Simons theory, Wilson loops and other defects, generalized geometry, higher Spin-structures, anomaly cancellation and various other aspects of quantum field theory.
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