A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections
High Energy Physics - Theory
2008-11-21 v1 Algebraic Geometry
Quantum Algebra
Abstract
Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual groups are equivalent. We reformulate this as a statement about categories of B-branes on the quantized moduli spaces of flat connections for these groups. We show that it implies the statement of the Quantum Geometric Langlands duality with a purely imaginary ``quantum parameter'' which is proportional to the inverse of the Planck constant of the gauge theory. The ramified version of the story is also considered.
Keywords
Cite
@article{arxiv.0811.3264,
title = {A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections},
author = {Anton Kapustin},
journal= {arXiv preprint arXiv:0811.3264},
year = {2008}
}
Comments
18 pages, AMS latex