Electric-magnetic duality and the geometric langlands program

Anton Kapustin, Edward Witten

Research output: Contribution to journalArticlepeer-review

445 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1-236
Number of pages236
JournalCommunications in Number Theory and Physics
Issue number1
StatePublished - Mar 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Mathematical Physics
  • General Physics and Astronomy


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