Recently, it has been shown that Geometric Langlands duality is closely related to properties of quantized supersymmetric Yang-Mills theory in four dimensions, as well as to Mirror Symmetry and Topological Field Theory. I will provide an introduction to these developments.

Literature

• A. Kapustin and E. Witten, Electric-Magnetic Duality and the Geometric Langlands Program, hep-th/0604151
• S.Gukov and E. Witten, Gauge Theory, Ramification, and the Geometric Langlands Program, hep-th/0612173
• A. Kapustin, Holomorphic reduction of \(N=2\) gauge theories, Wilson-'t Hooft operators, and S-duality, hep-th/0612119.

For some background, the following papers are very useful:

• E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988) 353.
• E. Witten, Mirror manifolds and Topological Field Theory, hep-th/9112056.