Quantum string integrability and AdS/CFT
- Creators
- Swanson, Ian
Abstract
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.
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.Attached Files
Submitted - 0410282.pdf
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Additional details
- Eprint ID
- 80502
- Resolver ID
- CaltechAUTHORS:20170816-143328990
- DE-FG03-92-ER40701
- Department of Energy (DOE)
- James A. Cullen Memorial Fund
- Created
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2017-08-16Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field