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arXiv · 0802.0999

Mirror Symmetry, Hitchin's Equations, And Langlands Duality

Edward Witten
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Abstract

Geometric Langlands duality can be understood from statements of mirror symmetry that can be formulated in purely topological terms for an oriented two-manifold $C$. But understanding these statements is extremely difficult without picking a complex structure on $C$ and using Hitchin's equations. We sketch the essential statements both for the ``unramified'' case that $C$ is a compact oriented two-manifold without boundary, and the ``ramified'' case that one allows punctures. We also give a few indications of why a more precise description requires a starting point in four-dimensional gauge theory.

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BibTeXRIS

Edward Witten. 2008-02-07. Mirror Symmetry, Hitchin's Equations, And Langlands Duality. https://doi.org/10.1093/acprof%3Aoso%2F9780199534920.003.0007

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