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A higher stacky perspective on Chern-Simons theory. (English) Zbl 1315.81091
Calaque, Damien (ed.) et al., Mathematical aspects of quantum field theories. Contributions of the les Houches winter school ‘Mathematical aspects of field theories’, Les Houches, France, January and February 2012. Cham: Springer (ISBN 978-3-319-09948-4/hbk; 978-3-319-09949-1/ebook). Mathematical Physics Studies, 153-211 (2015).
Summary: 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.
For the entire collection see [Zbl 1305.81009].

81T45 Topological field theories in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
58J28 Eta-invariants, Chern-Simons invariants
81T70 Quantization in field theory; cohomological methods
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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