Quantization via Mirror Symmetry

2010/11/09 by Sergei Gukov, Gukov, Sergei · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1011.2218

openalex publication_date 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Self-Duality Equations on a Riemann Surface
• Vector bundles on curves and generalized theta functions: recent results and open problems

Cited by

• Chern-Simons Theory and S-duality
• Equivariant Verlinde formula from fivebranes and vortices
• Complex Path Integrals and the Space of Theories

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