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Electric-Magnetic Duality And The Geometric Langlands Program

Anton Kapustin·Edward Witten
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Abstract

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.

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Anton Kapustin, Edward Witten. 2007-01-16. Electric-Magnetic Duality And The Geometric Langlands Program. https://arxiv.org/abs/hep-th/0604151

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