∞-Chern–Simons theory
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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.[1] The theory is named after Shiing-Shen Chern and James Simons, who first described Chern–Simons forms in 1974,[2] although the generalization was not developed by them.
See also
Literature
- Fiorenza, Domenico; Schreiber, Urs; Stasheff, Jim (2012). "Čech cocycles for differential characteristic classes: An ∞-Lie theoretic construction". Advances in Theoretical and Mathematical Physics 16: 149–250. doi:10.4310/ATMP.2012.v16.n1.a5.
- Schreiber, Urs (2011-11-16). "Chern-Simons terms on higher moduli stacks". Hausdorff Institute Bonn. https://ncatlab.org/schreiber/files/Bonn2011Schreiber.pdf.
- Schreiber, Urs (2013-10-29) (in en). Differential cohomology in a cohesive ∞-topos. https://ncatlab.org/schreiber/files/dcct170811.pdf.
- Domenico Fiorenza; Hisham Sati; Urs Schreiber (2011-12-07). "A Higher Stacky Perspective on Chern–Simons Theory". Mathematical Aspects of Quantum Field Theories. Mathematical Physics Studies. pp. 153–211. doi:10.1007/978-3-319-09949-1_6. ISBN 978-3-319-09948-4.
References
- ↑ Definition in Schreiber 2013, 1.2.6.5.2
- ↑ Chern, Shiing-Shen; Simons, James (September 1996). "Characteristic forms and geometric invariants" (in en). World Scientific Series in 20th Century Mathematics 4: 363–384. doi:10.1142/9789812812834_0026. ISBN 978-981-02-2385-4.
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