On the Integrability of String Theory in AdS_5 x S^5

Abstract

Integrability occupies an increasingly important role in direct tests of the AdS/CFT correspondence. Integrable structures have appeared in both planar N=4 super Yang-Mills theory and type IIB superstring theory on AdS_5 x S^5. A generalized statement of the AdS/CFT conjecture has therefore emerged in which, in addition to string energies corresponding to gauge theory anomalous dimensions, an infinite tower of higher charges on each side of the duality should also be equated. Demonstrations of this larger equivalence have been successful in certain regimes. To test this correspondence in a more stringent setting, the bosonic sector of the fully quantized string theory on AdS_5 x S^5 is expanded about the pp-wave limit to sextic order in fields, or to O(1/J^2), where J is the (large) angular momentum of string states boosted along an equatorial geodesic in the S^5 subspace. To avoid issues of renormalization, the analysis is restricted to zeroth order in the modified 't Hooft coupling where consistency conditions demand that integrability be realized. The string theory, however, fails to meet these conditions. This signals a potential problem with higher-order corrections in the large-J expansion around the pp-wave limit.

arXiv commentv2: corrections and improvements; v3: small correction to section 3; 20 pages, LaTeX

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Cited by in corpus (9)

• Yang-Mills Correlation Functions from Integrable Spin Chains
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• 1/J corrections to semiclassical AdS/CFT states from quantum Landau-Lifshitz model
• Quantum string integrability and AdS/CFT
• Spin Models and Superconformal Yang-Mills Theory
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
• New aspects of the BMN correspondence beyond the planar limit
• Sugawara form for AdS superstring