Gauge Theory and the Analytic Form of the Geometric Langlands Program
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.
Keywords
Cite
@article{arxiv.2107.01732,
title = {Gauge Theory and the Analytic Form of the Geometric Langlands Program},
author = {Davide Gaiotto and Edward Witten},
journal= {arXiv preprint arXiv:2107.01732},
year = {2022}
}
Comments
111 pp, minor clarifications in v.3 and a new appendix with more complete gauge theory analysis of why the classical Hitchin Hamiltonians can be quantized, minor corrections v. 4