Gauge Theory and Langlands Duality

Details Gauge Theory and Langlands Duality Gauge Theory and Langlands Duality

2009-06-15

arxiv.org/abs/0906.2747v1

Mathematics

Representation Theory

32 pages. Text of Bourbaki Seminar given by the author on June 13, 2009

Scientific paper

The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent works have already led to striking new insights into the geometric Langlands Program, which in particular involve the Homological Mirror Symmetry of the Hitchin moduli spaces of Higgs bundles on algebraic curves associated to two Langlands dual Lie groups.

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