Quantizing Derived Mapping Stacks

Abstract

In this review we discuss several topological and geometric invariants obtained by quantizing $\sigma$-models. More precisely, we don't quantize the entire mapping stack of fields, but rather only the substack of low energy fields. The theory restricted to this substack can be presented Lie theoretically and the problem is reduced to perturbative gauge theory. Throughout, we make extensive use of derived symplectic geometry and the BV formalism of Costello and Gwilliam. Finally, we frame the AJ Conjecture in knot theory as a question of quantizing character stacks.

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References in corpus (42)

• Deformation quantization of Poisson manifolds, I
• The Geometry of the Master Equation and Topological Quantum Field Theory
• A path integral approach to the Kontsevich quantization formula
• Lie theory for nilpotent L-infinity algebras
• Chiral de Rham complex
• On the characteristic and deformation varieties of a knot
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Perturbative quantum gauge theories on manifolds with boundary
• Lectures on curved beta-gamma systems, pure spinors, and anomalies
• Classical BV theories on manifolds with boundary
• Loop Spaces and Connections
• Skein modules of 3-manifolds
• Batalin-Vilkovisky formalism in the functional approach to classical field theory
• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
• Introduction to supergeometry
• Multiple Derived Lagrangian Intersections
• Lagrangian structures on mapping stacks and semi-classical TFTs
• Algebroid Yang-Mills Theories
• Twisted supergravity and its quantization
• On the AKSZ formulation of the Poisson sigma model
• Batalin-Vilkovisky quantization and the algebraic index
• Lie Algebroid Yang Mills with Matter Fields
• Ricci flow, Courant algebroids, and renormalization of Poisson--Lie T-duality
• Bimodules and branes in deformation quantization
• On the B-twisted topological sigma model and Calabi-Yau geometry
• Curving Yang-Mills-Higgs Gauge Theories
• Split Chern-Simons theory in the BV-BFV formalism
• Towards holography in the BV-BFV setting
• A cellular topological field theory
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• The Virasoro vertex algebra and factorization algebras on Riemann surfaces
• Character varieties, A-polynomials, and the AJ Conjecture
• Asymptotic Freedom in the BV Formalism
• Degenerate Classical Field Theories and Boundary Theories
• BV quantization of the Rozansky-Witten model
• Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor
• Deformation quantization of submanifolds and reductions via Duflo-Kirillov-Kontsevich map
• A model for complex analytic equivariant elliptic cohomology from quantum field theory
• All roots of unity are detected by the A-polynomial
• A holography theory of Poisson sigma model and deformation quantization
• Poisson sigma model and semiclassical quantization of integrable systems