Gauge Theory and the Analytic Form of the Geometric Langlands Program

Davide Gaiotto; Edward Witten

doi:10.1007/s00023-022-01225-6

Gauge Theory and the Analytic Form of the Geometric Langlands Program

Davide Gaiotto, Edward Witten

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	557-671
Number of pages	115
Journal	Annales Henri Poincare
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s00023-022-01225-6
State	Published - Jan 2024
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-022-01225-6

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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 {\textquoteright}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.",

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Gauge Theory and the Analytic Form of the Geometric Langlands Program

Abstract

All Science Journal Classification (ASJC) codes

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