An article that we wrote for a book on mathematical aspects of quantum field theory:
Domenico Fiorenza, Hisham Sati, Urs Schreiber,
A higher stacky perspective on Chern-Simons theory
in
Damien Calaque et al. (eds.)
Mathematical Aspects of Quantum Field Theories
Springer 2014
on Chern-Simons theory viewed in higher geometry with an outlook on ∞-Chern-Simons theory and its ∞-geometric prequantization.
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.
This article is part of the research laid out in the following related articles.
differential cohomology in a cohesive topos
A higher stacky perspective on Chern-Simons theory
For more discussion of higher category theory and physics see also the collection
For lecture notes on material closely related to the above article see also
For further discussion of applications in string theory/M-theory see