Contents Online
Communications in Number Theory and Physics
Volume 1 (2007)
Number 1
Electric-magnetic duality and the geometric Langlands program
Pages: 1 – 236
DOI: https://dx.doi.org/10.4310/CNTP.2007.v1.n1.a1
Authors
Abstract
The geometric Langlands program can be described in a natural way bycompactifying on a Riemann surface $C$ a twisted version of${\EUN}=4$ super Yang-Mills theory in four dimensions. The keyingredients are electric-magnetic duality of gauge theory, mirrorsymmetry of sigma-models, branes, Wilson and ’t Hooft operators,and topological field theory. Seemingly esoteric notions of thegeometric Langlands program, such as Hecke eigensheaves and ${\calD}$-modules, arise naturally from the physics.
Published 1 January 2007