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Advances in High Energy Physics
Volume 2010 (2010), Article ID 471238, 133 pages
http://dx.doi.org/10.1155/2010/471238
Review Article

On String Integrability: A Journey through the Two-Dimensional Hidden Symmetries in the AdS/CFT Dualities

Nordic Institute for Theoretical Physics (NORDITA), Roslagstullsbacken 23, 10691 Stockholm, Sweden

Received 28 February 2010; Accepted 9 March 2010

Academic Editor: Carlos Nunez

Copyright © 2010 Valentina Giangreco Marotta Puletti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, that is, the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensional 𝜎-models and in the AdS/CFT context. The first part is focused on the AdS5/CFT4 duality, especially the classical and quantum integrability of the type IIB superstring on AdS5×S5 which is discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to the AdS4/CFT3 duality with particular attention to the type IIA superstring on AdS4×𝑃3 and its integrability. This review is based on the author's PhD thesis discussed at Uppsala University the 21st September 2009.