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Abstract: We review the approach to the geometric Langlands program for algebraiccurves 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 furtherdevelopments. Placing this four dimensional gauge theory into a six dimensionalframework, as advocated by Witten, holds the promise to lead to a formulationwhich makes geometric Langlands duality a manifest symmetry like coavariancein differential geometry. Furthermore, it leads to an approach towardgeometric Langlands duality for algebraic surfaces, reproducing and extendingthe recent results of Braverman and Finkelberg.



Author: Karl-Georg Schlesinger

Source: https://arxiv.org/







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