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

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.

18 pages, AMS latex

References in corpus (4)

• H(3)+ correlators from Liouville theory
• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• Gauge Theory, Ramification, And The Geometric Langlands Program
• A-branes and Noncommutative Geometry

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• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• Surface operators in four-dimensional topological gauge theory and Langlands duality
• Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory
• Quasi-Topological Gauged Sigma Models, The Geometric Langlands Program, And Knots
• Quantum Analytic Langlands Correspondence
• AP Theory IV: Intrinsic Topological Quantum Langlands Theory