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Quantum string integrability and AdS/CFT

Swanson, Ian (2005) Quantum string integrability and AdS/CFT. Nuclear Physics B, 709 (3). pp. 443-464. ISSN 0550-3213. doi:10.1016/j.nuclphysb.2005.01.003.

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Recent explorations of the AdS/CFT correspondence have unveiled integrable structures underlying both planar N=4 super-Yang–Mills theory and type IIB string theory on AdS_5×S^5. Integrability in the gauge theory emerges from the fact that the dilatation generator can be identified with the Hamiltonian of an integrable quantum spin chain, and the classical string theory has been shown to contain infinite towers of hidden currents, a typical signature of integrability. Efforts to match the integrable structures of various classical string configurations to those of corresponding gauge theory quantum spin chains have been largely successful. By studying a semiclassical expansion about a class of point-like solitonic solutions to the classical string equations of motion on AdS_5×S^5, we take a step toward demonstrating that integrability in the string theory survives quantum corrections beyond tree level. Quantum fluctuations are chosen to align with background curvature corrections to the pp-wave limit of AdS_5×S5, and we present evidence for an infinite tower of local bosonic charges that are conserved by the quantum theory to quartic order in the expansion. We explicitly compute several higher charges based on a Lax representation of the worldsheet sigma model and provide a prescription for matching the eigenvalue spectra of these charges with corresponding quantities descending from the integrable structure of the gauge theory.

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Additional Information:© 2005 Elsevier B.V. Received 19 November 2004, Accepted 5 January 2005, Available online 19 January 2005. This article is registered under preprint number /hep-th/0410282. We would like to thank Curtis Callan for guidance and for reading the manuscript. We also thank Sergey Frolov, Vladimir Kazakov, Tristan McLoughlin, Andrei Mikhailov, John Schwarz and Arkady Tseytlin for many helpful discussions, The Ohio State University and the Institute for Advanced Study for hospitality, and the James A. Cullen Memorial Fund for support. This work was supported in part by US Department of Energy grant DE-FG03-92-ER40701.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
James A. Cullen Memorial FundUNSPECIFIED
Issue or Number:3
Classification Code:PACS: 11.15.-q; 11.25.-w; 11.25.Hf
Record Number:CaltechAUTHORS:20170816-143328990
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Official Citation:Ian Swanson, Quantum string integrability and AdS/CFT, Nuclear Physics B, Volume 709, Issue 3, 14 March 2005, Pages 443-464, ISSN 0550-3213, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80502
Deposited By: Tony Diaz
Deposited On:16 Aug 2017 21:49
Last Modified:15 Nov 2021 19:36

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