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

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dc.creatorKapustin, Anton
dc.date2008-11-20
dc.date.accessioned2026-07-07T10:19:43Z
dc.date.available2026-07-07T10:19:43Z
dc.descriptionMontonen-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.
dc.description18 pages, AMS latex
dc.identifierhttps://arxiv.org/abs/0811.3264
dc.identifierhttp://arxiv.org/abs/0811.3264
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174611
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subjectQuantum Algebra
dc.titleA Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections
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