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Branes and quantization

Gukov, Sergei and Witten, Edward (2009) Branes and quantization. Advances in Theoretical and Mathematical Physics, 13 (5). pp. 1445-1518. ISSN 1095-0761. https://resolver.caltech.edu/CaltechAUTHORS:20101108-100406383

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Abstract

The problem of quantizing a symplectic manifold (M,ω) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,ω) is the space of (B_(cc), B) strings, where B_(cc) and B are two A-branes; B is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B is supported on M, and the choice of ω is encoded in the choice of B_(cc). As an example, we describe from this point of view the representations of the group SL(2,R). Another application is to Chern–Simons gauge theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://projecteuclid.org/euclid.atmp/1282054099PublisherArticle
http://dx.doi.org/10.4310/ATMP.2009.v13.n5.a5DOIArticle
http://intlpress.com/site/pub/pages/journals/items/atmp/content/vols/0013/0005/a005/index.htmlPublisherArticle
http://arxiv.org/abs/0809.0305arXivDiscussion Paper
ORCID:
AuthorORCID
Gukov, Sergei0000-0002-9486-1762
Witten, Edward0000-0002-7752-6073
Additional Information:© 2009 International Press. We would like to thank D. Kazhdan, M. Kontsevich, N. Hitchin, and P. Sarnak for valuable discussions. Research of SG is supported in part by NSF Grants DMS-0635607 and PHY-0757647, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is supported in part by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.
Funders:
Funding AgencyGrant Number
NSFDMS-0635607
NSFPHY-0757647
Russian Foundation for Basic Research07- 02-00645
Alfred P. Sloan FoundationUNSPECIFIED
NSFPHY-0503584
Issue or Number:5
Record Number:CaltechAUTHORS:20101108-100406383
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20101108-100406383
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20708
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:29 Nov 2010 19:04
Last Modified:09 Mar 2020 13:18

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