Special Feature: The Takagi Lectures

Japanese Journal of Mathematics

, Volume 6, Issue 2, pp 65-119

First online:

Quantization via mirror symmetry

  • Sergei GukovAffiliated withCalifornia Institute of TechnologyMax-Planck-Institut für Mathematik Email author 

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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.

Keywords and phrases

mirror symmetry derived category branes quantization symplectic geometry

Mathematics Subject Classification (2010)

18F20 51P05 81S10