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Surface operators in four-dimensional topological gauge theory and Langlands duality

Kapustin, Anton and Setter, Kevin and Vyas, Ketan (2010) Surface operators in four-dimensional topological gauge theory and Langlands duality. . (Submitted)

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We study surface and line operators in the GL-twisted N = 4 gauge theory in four dimensions. Their properties depend on the parameter t which determines the BRST operator of theory. For t = i we propose a complete description of the 2-category of surface operators in terms of module categories. We also determine the monoidal category of line operators which includes Wilson lines as special objects. For t = 1 and t = 0 we only discuss surface and line operators in the abelian case. Applications to the categorification of the local geometric Langlands duality and its quantum version are briefly described. In the appendices we discuss several 3d and 2d topological field theories with gauge fields. In particular, we explain a relationship between the category of branes in the gauged B-model and the equivariant derived category of coherent sheaves.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:(Submitted on 2 Feb 2010) A.K. would like to thank R. Bezrukavnikov, A. Braverman, D. Orlov, V. Lunts and especially L. Rozansky for useful discussions. K.S. acknowledges the support of the Jack Kent Cooke Foundation. This work was supported in part by the DOE grant DE-FG02-92ER40701.
Funding AgencyGrant Number
Jack Kent Cooke FoundationUNSPECIFIED
Department of Energy (DOE)DE-FG02-92ER40701
Record Number:CaltechAUTHORS:20160503-145417819
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66624
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 04:40
Last Modified:03 Oct 2019 09:58

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