Gauge Theory and the Analytic Form of the Geometric Langlands Program

Davide Gaiotto, Edward Witten

Research output: Contribution to journalArticlepeer-review

Abstract

We present a gauge-theoretic interpretation of the “analytic” version of the geometric Langlands program, in which Hitchin Hamiltonians and Hecke operators are viewed as concrete operators acting on a Hilbert space of quantum states. The gauge theory ingredients required to understand this construction—such as electric–magnetic duality between Wilson and ’t Hooft line operators in four-dimensional gauge theory—are the same ones that enter in understanding via gauge theory the more familiar formulation of geometric Langlands, but now these ingredients are organized and applied in a novel fashion.

Original languageEnglish (US)
JournalAnnales Henri Poincare
DOIs
StateAccepted/In press - 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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