A Note on Quantum Geometric Langlands Duality, Gauge Theory, and Quantization of the Moduli Space of Flat Connections - High Energy Physics - TheoryReport as inadecuate




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Abstract: Montonen-Olive duality implies that the categories of A-branes on the modulispaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dualgroups are equivalent. We reformulate this as a statement about categories ofB-branes on the quantized moduli spaces of flat connections for these groups.We show that it implies the statement of the Quantum Geometric Langlandsduality with a purely imaginary ``quantum parameter- which is proportional tothe inverse of the Planck constant of the gauge theory. The ramified version ofthe story is also considered.



Author: Anton Kapustin

Source: https://arxiv.org/







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