Quantization via Mirror Symmetry

Abstract

When combined with mirror symmetry, the A-model approach to quantization leads to a fairly simple and tractable problem. The most interesting part of the problem then becomes finding the mirror of the coisotropic brane. We illustrate how it can be addressed in a number of interesting examples related to representation theory and gauge theory, in which mirror geometry is naturally associated with the Langlands dual group. Hyperholomorphic sheaves and (B,B,B) branes play an important role in the B-model approach to quantization.

44 pp

References in corpus (11)

• Mirror symmetry, Langlands duality, and the Hitchin system
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Remarks on A-branes, Mirror Symmetry, and the Fukaya category
• The Modular Group Action on Real SL(2)-characters of a One-Holed Torus
• Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence
• Vector bundles on curves and generalized theta functions: recent results and open problems
• A New Look At The Path Integral Of Quantum Mechanics
• Coisotropic Branes, Noncommutativity, and the Mirror Correspondence
• Geometry of the moduli space of Higgs bundles
• Geometric Langlands And The Equations Of Nahm And Bogomolny
• Hyperholomorphic sheaves and new examples of hyperkaehler manifolds

Cited by in corpus (7)

• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Chern-Simons Theory and S-duality
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Equivariant Verlinde formula from fivebranes and vortices
• Complex Path Integrals and the Space of Theories
• Symmetries of 2d TQFTs and Equivariant Verlinde Formulae for General Groups
• Coisotropic Branes in Toric Calabi-Yau 3-folds