Branes and Quantization

Abstract

The problem of quantizing a symplectic manifold (M,ω) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,ω) is the space of (Bcc,B') strings, where Bcc and B' are two A-branes; B' is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B' is supported on M, and the choice of ωis encoded in the choice of Bcc. As an example, we describe from this point of view the representations of the group SL(2,R). Another application is to Chern-Simons gauge theory.

70 pp, v2: references added

Cited by in corpus (39)

• Solving the Schwarzian via the Conformal Bootstrap
• Holomorphic Blocks in Three Dimensions
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Deformation quantization and superconformal symmetry in three dimensions
• Gravitational Edge Modes, Coadjoint Orbits, and Hydrodynamics
• Ω-deformation and quantization
• Edge Dynamics from the Path Integral: Maxwell and Yang-Mills
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• The Celestial Chiral Algebra of Self-Dual Gravity on Eguchi-Hanson Space
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Teichmuller TQFT vs Chern-Simons Theory
• Splitting of surface defect partition functions and integrable systems
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Matrix Quantization of Gravitational Edge Modes
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• A 3d-3d appetizer
• Surface defects in gauge theory and KZ equation
• Higher U(1)-gerbe connections in geometric prequantization
• Quantization of Emergent Gravity
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
• On quantization of complex symplectic manifolds
• Comparing Poisson Sigma Model with A-model
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Brane quantization of toric Poisson varieties
• Rank two nilpotent co-Higgs sheaves on complex surfaces
• Bispectral duality and separation of variables from surface defect transition
• Batalin--Vilkovisky quantization and supersymmetric twists
• Branes and DAHA Representations
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Secondary products in supersymmetric field theory
• Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
• Quantizable functions on Kähler manifolds and non-formal quantization
• Line Operators in 4d Chern-Simons Theory and Cherkis Bows
• Time evolution of density matrices as a theory of random surfaces
• Quantization in Cartesian coordinates and the Hofer metric
• Quantization via Deformation of Prequantization
• Instances of Higher Geometry in Field Theory
• Non-orientable surfaces and electric-magnetic duality
• Torus actions on free associative algebras, lifting and Białynicki-Birula type theorems