∞-Chern–Simons theory
{{Short description|Combination of higher category theory with Chern–Simons theory}}
In mathematics, ∞-Chern–Simons theory (not to be confused with infinite-dimensional Chern–Simons theory) is a generalized formulation of Chern–Simons theory from differential geometry using the formalism of higher category theory, which in particular studies ∞-categories. It is obtained by taking general abstract analogs of all involved concepts defined in any cohesive ∞-topos, for example that of smooth ∞-groupoids. Principal bundles on which Lie groups act are for example replaced by ∞-principal bundles on with group objects in ∞-topoi act.Definition in Schreiber 2013, 1.2.6.5.2 The theory is named after Shiing-Shen Chern and James Simons, who first described Chern–Simons forms in 1974,{{cite journal |last1=Chern |first1=Shiing-Shen |author-link1=Shiing-Shen Chern |last2=Simons |first2=James |author-link2=Jim Simons |date=September 1996 |title=Characteristic forms and geometric invariants |journal=World Scientific Series in 20th Century Mathematics |language=en |volume=4 |pages=363–384 |doi=10.1142/9789812812834_0026|isbn=978-981-02-2385-4 }} although the generalization was not developed by them.
See also
Literature
- {{cite arXiv |eprint=1011.4735 |author1=Domenico Fiorenza |author2=Urs Schreiber |author3=Jim Stasheff |title=Cech cocycles for differential characteristic classes -- An infinity-Lie theoretic construction |date=2011-06-08|class=math.AT }}
- {{cite conference |last=Schreiber |first=Urs |author-link=Urs Schreiber |title=Chern-Simons terms on higher moduli stacks |url=https://ncatlab.org/schreiber/files/Bonn2011Schreiber.pdf |conference=Hausdorff Institute Bonn |publication-date=2011-11-16}}
- {{cite book |last=Schreiber |first=Urs |author-link=Urs Schreiber |url=https://ncatlab.org/schreiber/files/dcct170811.pdf |title=Differential cohomology in a cohesive ∞-topos |publisher= |isbn= |location= |publication-date=2013-10-29 |language=en}}
- {{cite book |arxiv=1301.2580 |author1=Domenico Fiorenza |author2=Hisham Sati |author3=Urs Schreiber |title=Mathematical Aspects of Quantum Field Theories |chapter=A Higher Stacky Perspective on Chern–Simons Theory |series=Mathematical Physics Studies |date=2011-12-07|pages=153–211 |doi=10.1007/978-3-319-09949-1_6 |isbn=978-3-319-09948-4 }}
References
External links
- [https://ncatlab.org/schreiber/show/infinity-Chern-Simons+theory infinity-Chern-Simons theory] on nLab