A higher stacky perspective on Chern-Simons theory
arXiv:1301.2580 · doi:10.1007/978-3-319-09949-1_6
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.
final version; exposition improved; a few typos corrected; 54 pages
References in corpus (15)
- Higher Topos Theory
- Generalised Geometry for M-Theory
- AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
- Principal infinity-bundles -- General theory
- Classical and quantum Lagrangian field theories with boundary
- Extended higher cup-product Chern-Simons theories
- L-infinity algebras of local observables from higher prequantum bundles
- Higher Symplectic Geometry
- AQFT from n-functorial QFT
- Generalizing Geometry - Algebroids and Sigma Models
- Characteristic classes associated to Q-bundles
- Topological Quantum Field Theories from Compact Lie Groups
- Relative quantum field theory
- Global gauge anomalies in two-dimensional bosonic sigma models
- Chern-Simons Theory with Wilson Lines and Boundary in the BV-BFV Formalism
Cited by in corpus (36)
- Notes on generalized global symmetries in QFT
- Extended higher cup-product Chern-Simons theories
- The WZW term of the M5-brane and differential cohomotopy
- Wannier functions and Z_2 invariants in time-reversal symmetric topological insulators
- Twisted Cohomotopy implies twisted String structure on M5-branes
- Homotopy colimits and global observables in Abelian gauge theory
- Twisted Cohomotopy implies M5-brane anomaly cancellation
- Lie n-algebras of BPS charges
- The stack of Yang-Mills fields on Lorentzian manifolds
- Ramond-Ramond fields and twisted differential K-theory
- Orbifolds by 2-groups and decomposition
- Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
- Abelian BF theory and Turaev-Viro invariant
- Gauge-theoretic invariants for topological insulators: A bridge between Berry, Wess-Zumino, and Fu-Kane-Mele
- Fluxes, bundle gerbes and 2-Hilbert spaces
- Quantization via Linear homotopy types
- Massey products in differential cohomology via stacks
- Primary operations in differential cohomology
- Ninebrane structures
- Bordism for the 2-group symmetries of the heterotic and CHL strings
- Spectral sequences in smooth generalized cohomology
- Global Double Field Theory is Higher Kaluza-Klein Theory
- Flux Quantization on 11-dimensional Superspace
- Flux Quantization on M5-branes
- Higher abelian gauge theory associated to gerbes on noncommutative deformed M5-branes and S-duality
- Derived stacks in symplectic geometry
- Higher prequantum geometry
- Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
- Twisted smooth Deligne cohomology
- Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields
- Proper Orbifold Cohomology
- Twisted differential KO-theory
- Engineering of Anyons on M5-Probes via Flux Quantization
- Parametrized geometric cobordism and smooth Thom stacks
- Gerbes in Geometry, Field Theory, and Quantisation
- Extended Field Theories as higher Kaluza-Klein theories