Electric-magnetic duality and the geometric Langlands program

2007/01/01 by Anton Kapustin, Edward Witten · 8 citations
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Advanced Algebra and Geometry #Langlands program #Langlands dual group #Duality (order theory) #Mathematics #Pure mathematics #Conjecture

paper · pdf · doi:10.4310/cntp.2007.v1.n1.a1

openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory. Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.

Citations

• Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
• Chiral de Rham complex and the half-twisted sigma-model
• A-branes and Noncommutative Geometry
• D-branes and K-theory in 2D topological field theory
• The Self-Duality Equations on a Riemann Surface
• K-Theory from a physical perspective
• Mirror Manifolds And Topological Field Theory
• Duality in Topological Quantum Field Theories
• Moduli of connections with a small parameter on a curve
• String theory and noncommutative geometry
• Mathai-Quillen formulation of twisted N = 4 supersymmetric gauge theories in four dimensions
• Supersymmetries and their representations
• The Geometry and Dynamics of Magnetic Monopoles
• Construction of instantons
• The Langlands program and string modular K3 surfaces
• Magnetic monopoles as gauge particles?
• Intersection homology theory
• Algebras, BPS states, and strings
• Baryons And Branes In Anti de Sitter Space
• On the phase transition towards permanent quark confinement
• Elliptic Calogero-Moser system from two dimensional current algebra
• Categorification and correlation functions in conformal field theory
• Langlands duality and G2 spectral curves
• Topological quantum field theory
• The Index of Elliptic Operators: I
• Fourier transform for D-algebras
• Topological reduction of 4D SYM to 2D σ-models
• Generalized Calabi-Yau Manifolds

Cited by

• Harmonic Cheeger–Simons characters with applications
• Argyres-Douglas theories, chiral algebras and wild Hitchin characters
• Mirror symmetry for the Painlevé character varieties
• Wall-crossing in coupled 2d-4d systems
• The world-sheet description of A and B branes revisited
• Derived categories and stacks in physics
• Classical integrable systems and gauge field theories
• Montonen–Olive duality [wikipedia]
• S-duality [wikipedia]