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arXiv · 1301.2580

A higher stacky perspective on Chern-Simons theory

Domenico Fiorenza·Hisham Sati·Urs Schreiber
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Abstract

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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Domenico Fiorenza, Hisham Sati, Urs Schreiber. 2013-12-07. A higher stacky perspective on Chern-Simons theory. https://doi.org/10.1007/978-3-319-09949-1_6

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