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December 28, 2012

A Higher Stacky Perspective On Chern-Simons Theory

Posted by Urs Schreiber

We are finalizing a contribution for a book on mathematical aspects of quantum field theory:

Domenico Fiorenza, Hisham Sati, Urs Schreiber,

A higher stacky perspective on Chern-Simons theory

Abstract. 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”, “mutli-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. At the end 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, generalized geometry, higher Spin-structures, anomaly cancellation and various other aspects of quantum field theory.

Comments are welcome! (See the pdf at the above link.)

Posted at December 28, 2012 3:19 PM UTC

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Re: A Higher Stacky Perspective On Chern-Simons Theory

Some typos:

p. 35 “arbitrary codimenion”

p. 38 “Its differntial refinement”

p. 39 “see also the exposition is in [79].”

p. 39 “is constrained to be by the restriction”

p. 40 “for ease discussion”

p. 43 “the mdouli stack”

p. 43 “background gaule field”

What’s motivating this comment

we will attempt to dissipate the false belief that higher toposes are an esoteric discipline whose secret rites are reserved to initiates?

Do you feel some prejudice is blocking its reception from both the mathematics and physics wings of mathematical physics? I guess, as ever, the solution is to resolve some problem that people who don’t know about higher toposes would like to see resolved.

Posted by: David Corfield on January 2, 2013 12:05 PM | Permalink | Reply to this

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