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.)

arXiv comment37 pp

References in corpus (6)

• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• The Character Theory of a Complex Group
• 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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• The Character Theory of a Complex Group
• On 2d TQFTs whose values are holomorphic symplectic varieties
• Twisted compactifications of 3d N = 4 theories and conformal blocks
• A manifestly MHV Lagrangian for N=4 Yang-Mills
• A note on Wilson-'t Hooft operators
• Supersymmetric Ground States of 3d $\mathcal{N}=4$ Gauge Theories on a Riemann Surface
• Quantization via Mirror Symmetry
• OPE of Wilson-'t Hooft operators in N=4 and N=2 SYM with gauge group G=PSU(3)
• Non-abelian vortices, Hecke modifications and singular monopoles
• Secondary products in supersymmetric field theory
• AP Theory IV: Intrinsic Topological Quantum Langlands Theory