Mikhailov, Andrei (2012) Symmetries of massless vertex operators in AdS_5 × S^5. Journal of Geometry and Physics, 62 (2). pp. 479-505. ISSN 0393-0440. doi:10.1016/j.geomphys.2011.09.002. https://resolver.caltech.edu/CaltechAUTHORS:20120402-132322403
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Abstract
The worldsheet sigma model of the superstring in AdS_5×S^5 has a one-parameter family of flat connections parametrized by the spectral parameter. The corresponding Wilson line is not BRST invariant for an open contour, because the BRST transformation leads to boundary terms. These boundary terms define a cohomological complex associated with the endpoint of the contour. We study the cohomology of this complex for Wilson lines in some infinitedimensional representations. We find that for these representations the cohomology is nontrivial at the ghost number 2. This implies that it is possible to define a BRST invariant open Wilson line. The central point in the construction is the existence of massless vertex operators transforming exactly covariantly under the action of the global symmetry group. In flat space, massless vertices transform covariantly only up to adding BRST-exact terms. But in AdS we show that it is possible to define vertices so that they transform exactly covariantly.
| Item Type: | Article | |||||||||
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| Additional Information: | © 2011 Published by Elsevier B.V. Received 13 July 2011. Accepted 3 September 2011. Available online 24 September 2011. I wish to thank Y. Aisaka, N.J. Berkovits, V. Serganova and B.C. Vallilo for many useful discussions. This research was supported by the Sherman Fairchild Fellowship and in part by the RFBR, Grant No. 06-02-17383, and also in part by a Russian grant for the support of scientific schools NSh-8065.2006.2. Part of this work was done during the Workshop ‘‘Non-perturbative methods in strongly coupled gauge theories’’, at the Galileo Galilei Institute for Theoretical Physics in Florence. I would like to thank the organizers of this workshop for their hospitality. Another part of this work was done during the Monsoon Workshop in TIFR, Mumbai. I wish to thank the organizers and the staff members at TIFR for their hospitality. Another part of this work was done during my stay at the IFT São Paulo; I wish to thank N.J. Berkovits for his hospitality. Another part of this work was done during the workshop ‘‘Fundamental Aspects of Superstring Theory’’ at KITP Santa Barbara; I wish to thank the organizers of the workshop for their hospitality. | |||||||||
| Group: | Caltech Theory | |||||||||
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| Subject Keywords: | Superstring; Pure spinor formalism; Lie algebra cohomology; AdS/CFT correspondence; Integrability | |||||||||
| Issue or Number: | 2 | |||||||||
| DOI: | 10.1016/j.geomphys.2011.09.002 | |||||||||
| Record Number: | CaltechAUTHORS:20120402-132322403 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120402-132322403 | |||||||||
| Official Citation: | Andrei Mikhailov, Symmetries of massless vertex operators in, Journal of Geometry and Physics, Volume 62, Issue 2, February 2012, Pages 479-505, ISSN 0393-0440, 10.1016/j.geomphys.2011.09.002. | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 29939 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 17 Apr 2012 20:52 | |||||||||
| Last Modified: | 09 Nov 2021 19:33 |
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