Geometric Langlands From Six Dimensions

Edward Witten

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arXiv · 0905.2720

Geometric Langlands From Six Dimensions

Edward Witten

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Abstract

Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally understood as a consequence of the existence of a certain exotic supersymmetric conformal field theory in six dimensions. The same six-dimensional theory also gives a useful framework for understanding some recent mathematical results involving a counterpart of geometric Langlands duality for complex surfaces. (This article is based on a lecture at the Raoul Bott celebration, Montreal, June 2008.)

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Edward Witten. 2009-05-17. Geometric Langlands From Six Dimensions. https://arxiv.org/abs/0905.2720

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