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Rigid Surface Operators

Gukov, Sergei and Witten, Edward (2010) Rigid Surface Operators. Advances in Theoretical and Mathematical Physics, 14 (1). pp. 87-178. ISSN 1095-0761. https://resolver.caltech.edu/CaltechAUTHORS:20160504-103840382

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/euclid.atmp/1283281759PublisherArticle
http://arxiv.org/abs/0804.1561arXivDiscussion Paper
http://dx.doi.org/10.4310/ATMP.2010.v14.n1.a3DOIArticle
ORCID:
AuthorORCID
Gukov, Sergei0000-0002-9486-1762
Witten, Edward0000-0002-7752-6073
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.
Funders:
Funding AgencyGrant Number
NSFDMS-0635607
Russian Foundation for Basic Research07-02-00645
Alfred P. Sloan FoundationUNSPECIFIED
NSFPHY-0503584
Issue or Number:1
Record Number:CaltechAUTHORS:20160504-103840382
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160504-103840382
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66644
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 May 2016 20:41
Last Modified:09 Mar 2020 13:18

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