A physics perspective on geometric Langlands duality

Details A physics perspective on geometric Langlands duality A physics perspective on geometric Langlands duality

2009-11-24

arxiv.org/abs/0911.4586v1

Physics

High Energy Physics

High Energy Physics - Theory

19 pages

Scientific paper

We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.

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