Geometric Langlands And The Equations Of Nahm And Bogomolny

Details Geometric Langlands And The Equations Of Nahm And Bogomolny Geometric Langlands And The Equations Of Nahm And Bogomolny

2009-05-29

arxiv.org/abs/0905.4795v2

Physics

High Energy Physics

High Energy Physics - Theory

37 pp

Scientific paper

Geometric Langlands duality relates a representation of a simple Lie group $G^\vee$ to the cohomology of a certain moduli space associated with the dual group $G$. In this correspondence, a principal $SL_2$ subgroup of $G^\vee$ makes an unexpected appearance. Why this happens can be explained using gauge theory, as we will see in this article, with the help of the equations of Nahm and Bogomolny. (Based on a lecture at Geometry and Physics: Atiyah 80, Edinburgh, April 2009.)

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