Poisson sigma models and deformation quantization

Abstract

This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.

11 pages

Cited by in corpus (48)

• Dilaton Gravity in Two Dimensions
• Fuzzy Complex Projective Spaces and their Star-products
• Brane Partons and Singleton Strings
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• On First Order Formalism in String Theory
• Dynamical actions and q-representation theory for double-scaled SYK
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Deformation independent open brane metrics and generalized theta parameters
• An action principle for Vasiliev's four-dimensional higher-spin gravity
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Generalized Poisson sigma models
• Formal symplectic groupoid
• Hamiltonian BRST deformation of a class of n-dimensional BF-type theories
• Lectures on mathematical aspects of (twisted) supersymmetric gauge theories
• Introduction to the BV-BFV formalism
• Dynamical noncommutativity
• Graph cohomology classes in the Batalin-Vilkovisky formalism
• Local Superfield Lagrangian BRST Quantization
• Consistent interactions of dual linearized gravity in D=5: couplings with a topological BF model
• Symplectic connections, Noncommutative Yang Mills theory and Supermembranes
• Noncommutativity in weakly curved background by canonical methods
• PT-symmetry breaking hamiltonian interactions in BF models
• Poisson reduction and branes in Poisson-Sigma models
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• On the Globalization of the Poisson Sigma Model in the BV-BFV Formalism
• Extending general covariance: Moyal-type noncommutative manifolds
• An Embedding of the BV Quantization into an N=1 Local Superfield Formalism
• On Dequantization of Fedosov's Deformation Quantization
• Histories and observables in covariant field theory
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Minimal models of quantum homotopy Lie algebras via the BV-formalism
• Jacobi sigma models
• Four-dimensional couplings among BF and massless Rarita-Schwinger theories: a BRST cohomological approach
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• Dimensional Reduction of Nonlinear Gauge Theories
• Self-interactions in a topological BF-type model in D=5
• Topological A-Type Models with Flux
• Couplings between a collection of BF models and a set of three-form gauge fields
• On the generalized Freedman-Townsend model
• First order gauge field theories from a superfield formulation
• Quantum group origins of edge states in double-scaled SYK
• Target Space Equivariant Cohomological Structure of the Poisson Sigma Model
• Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
• On the inverse mapping of the formal symplectic groupoid of a deformation quantization
• Topological and dynamical aspects of Jacobi sigma models
• A note on Q-algebra and quantization
• The Quantum Darboux Theorem,
• Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes