A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections

Details A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections

2008-11-20

arxiv.org/abs/0811.3264v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, AMS latex

Scientific paper

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.

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