Quasi-Hamiltonian reduction via classical Chern-Simons theory
arXiv:1311.6429 · doi:10.1016/j.aim.2015.09.031
Abstract
This paper puts the theory of quasi-Hamiltonian reduction in the framework of shifted symplectic structures developed by Pantev, Toën, Vaquié and Vezzosi. We compute the symplectic structures on mapping stacks and show how the AKSZ topological field theory defined by Calaque allows one to neatly package the constructions used in quasi-Hamiltonian reduction. Finally, we explain how a prequantization of character stacks can be obtained purely locally.
arXiv comment33 pages
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Cited by in corpus (18)
- Lagrangian structures on mapping stacks and semi-classical TFTs
- Multiple Derived Lagrangian Intersections
- Shifted cotangent stacks are shifted symplectic
- Calabi-Yau structures on topological Fukaya categories
- Stacky Hamiltonian actions and symplectic reduction
- Symplectic implosion and the Grothendieck-Springer resolution
- Derived Algebraic Geometry
- Shifted Symplectic and Poisson Structures on Spaces of Framed Maps
- Shifted symplectic reduction of derived critical loci
- Derived stacks in symplectic geometry
- Calabi-Yau structures for multiplicative preprojective algebras
- Shifted coisotropic structures for differentiable stacks
- Gaiotto's Lagrangian subvarieties via derived symplectic geometry
- Calabi-Yau structures on (quasi-)bisymplectic algebras
- Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
- Gerbes in Geometry, Field Theory, and Quantisation
- Derived symplectic geometry
- From multiplicative to additive geometry: Deformation theory and 2D TQFT