Published October 2009
| Published
Journal Article
Open
Branes and quantization
- Creators
-
Gukov, Sergei
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Witten, Edward
Chicago
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.
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.Attached Files
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Additional details
- Eprint ID
- 20708
- Resolver ID
- CaltechAUTHORS:20101108-100406383
- NSF
- DMS-0635607
- NSF
- PHY-0757647
- Russian Foundation for Basic Research
- 07- 02-00645
- Alfred P. Sloan Foundation
- NSF
- PHY-0503584
- Created
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2010-11-29Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field