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Published January 2010 | Submitted + Published
Journal Article Open

Rigid Surface Operators

Abstract

Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang–Mills theory, and determined how they transform under S-duality. Those surface operators depend on a relatively large number of freely adjustable parameters. In the present paper, we consider the opposite case of half-BPS surface operators that are "rigid" in the sense that they do not depend on any parameters at all. We present some simple constructions of rigid half-BPS surface operators and attempt to determine how they transform under duality. This attempt is only partially successful, suggesting that our constructions are not the whole story. The partial match suggests interesting connections with quantization. We discuss some possible refinements and some string theory constructions which might lead to a more complete picture.

Additional Information

© 2010 International Press. We would like to thank R. Bezrukavnikov, A. Braverman, A. Elashvili, D. Gaiotto, V. Kac, G. Lusztig, C. Vafa, and especially D. Kazhdan for valuable discussions and correspondence. Research of SG is supported in part by NSF Grant DMS-0635607, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is partly supported by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.

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Published - euclid.atmp.1283281759.pdf

Submitted - 0804.1561.pdf

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August 19, 2023
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