Mirror symmetry and deformation quantization

Abstract

The paper is devoted to the comparison of the Fukaya category (it is responcible for the A-side of mirror symmetry) with the category of holonomic modules over the quantized algebra of functions on the same symplectic manifold. We conjecture that these categories become $A_{\infty }$-equivalent after a twist by a kind of integral transformation.

References in corpus (7)

• Deformation quantization of Poisson manifolds, I
• Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields
• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• Deformations of algebras over operads and Deligne's conjecture
• Fukaya category and Fourier transform
• Mirror symmetry for abelian varieties
• D-branes in a topologically nontrivial B-field

Cited by in corpus (10)

• Topological strings on noncommutative manifolds
• A-branes and Noncommutative Geometry
• A New Look At The Path Integral Of Quantum Mechanics
• Complex Path Integrals and the Space of Theories
• Cohomological constraint to deformations of compact Kaehler manifolds
• Stacks of quantization-deformation modules on complex symplectic manifolds
• On higher rank coisotropic A-branes
• Balanced metrics and noncommutative Kaehler geometry
• Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces
• Bohr-Sommerfeld Star Products