Geometric Langlands And The Equations Of Nahm And Bogomolny

Abstract

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 $S{L}_2$ 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.)

37 pp

References in corpus (3)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Electric-Magnetic Duality And The Geometric Langlands Program
• The 't Hooft-Polyakov Monopole in the Presence of a 't Hooft Operator

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• OPE of Wilson-'t Hooft operators in N=4 and N=2 SYM with gauge group G=PSU(3)
• AP Theory IV: Intrinsic Topological Quantum Langlands Theory