Matching Higher Conserved Charges for Strings and Spins

Abstract

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.

Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references added

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• Spinning strings in AdS_5 x S^5 and integrable systems
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Precision Spectroscopy of AdS/CFT
• Yang-Mills Duals for Semiclassical Strings
• Higher loops, integrability and the near BMN limit
• Non-local charges on AdS_5 x S^5 and PP-waves
• Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators

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