Japanese Journal of Mathematics

, Volume 6, Issue 2, pp 65–119

Quantization via mirror symmetry

Special Feature: The Takagi Lectures

DOI: 10.1007/s11537-011-1033-2

Cite this article as:
Gukov, S. Jpn. J. Math. (2011) 6: 65. doi:10.1007/s11537-011-1033-2


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.

Keywords and phrases

mirror symmetry derived category branes quantization symplectic geometry 

Mathematics Subject Classification (2010)

18F20 51P05 81S10 

Copyright information

© The Mathematical Society of Japan and Springer Japan 2011

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Max-Planck-Institut für MathematikBonnGermany

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