Electric-Magnetic Duality And The Geometric Langlands Program

@article{Kapustin2006ElectricMagneticDA,
  title={Electric-Magnetic Duality And The Geometric Langlands Program},
  author={A. Kapustin and E. Witten},
  journal={Communications in Number Theory and Physics},
  year={2006},
  volume={1},
  pages={1-236}
}
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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