Electric-Magnetic Duality And The Geometric Langlands Program
Anton Kapustin, Edward Witten
TL;DR
This paper explains how the geometric Langlands program can be understood through the lens of four-dimensional N=4 super Yang-Mills theory compactified on a Riemann surface, highlighting the role of electric-magnetic duality and related concepts.
Contribution
It provides a physical interpretation of the geometric Langlands program using gauge theory, dualities, and topological field theory, connecting abstract mathematics with physical theories.
Findings
Geometric Langlands arises naturally from 4D super Yang-Mills theory.
Electric-magnetic duality explains key structures like Hecke eigensheaves.
Physical concepts illuminate the mathematical framework of the Langlands program.
Abstract
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.
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Taxonomy
TopicsSolar and Space Plasma Dynamics · Geomagnetism and Paleomagnetism Studies