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Geometric Langlands From Six Dimensions

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 exot...

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Detalles Bibliográficos
Autor principal: Witten, Edward
Lenguaje:eng
Publicado: 2010
Materias:
Acceso en línea:http://cds.cern.ch/record/1177958
Descripción
Sumario: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.)