Quasi-Hamiltonian reduction via classical Chern-Simons theory

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.

33 pages

References in corpus (4)

• Higher and derived stacks: a global overview
• Iterated spans and classical topological field theories
• S^1-Equivariant simplicial algebras and de Rham theory
• Hamiltonian reduction and Maurer-Cartan equations

Cited by in corpus (16)

• 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
• Shifted Symplectic and Poisson Structures on Spaces of Framed Maps
• Derived Algebraic Geometry
• Derived stacks in symplectic geometry
• Shifted symplectic reduction of derived critical loci
• Calabi-Yau structures for multiplicative preprojective algebras
• Gaiotto's Lagrangian subvarieties via derived symplectic geometry
• Shifted coisotropic structures for differentiable stacks
• Gerbes in Geometry, Field Theory, and Quantisation
• Derived symplectic geometry
• Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
• Calabi-Yau structures on (quasi-)bisymplectic algebras
• From multiplicative to additive geometry: Deformation theory and 2D TQFT