Spin chains and string theory

Abstract

Recently, an impressive agreement was found between anomalous dimensions of certain operators in N=4 SYM and rotating strings with two angular momenta in the bulk of AdS5xS5. A one-loop field theory computation, which involves solving a Heisenberg chain by means of the Bethe ansatz agrees with the large angular momentum limit of a rotating string. We point out that the Heisenberg chain can be equally well solved by using a sigma model approach. Moreover we also show that a certain limit, akin to the BMN limit, leads exactly to the same sigma model for a string rotating with large angular momentum. The agreement is then at the level of the action. As an upshot we propose that the rotating string should be identified with a coherent, semi-classical state built out of the eigenstates of the spin chain. The agreement is then complete. For example we show that the mean value of the spin <S> gives, precisely, the position of the string in the bulk. This suggests a more precise formulation of the AdS/CFT correspondence in the large-N limit and also indicates a way to obtain string theory duals of other gauge theories.

16 pages. LaTeX. v2: References and some comments added. v3: References to more recent work added

References in corpus (11)

• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Matching Higher Conserved Charges for Strings and Spins
• Precision Spectroscopy of AdS/CFT
• Spinning strings and AdS/CFT duality
• The SU(3) spin chain sigma model and string theory
• Speeding Strings
• A note on spin chain/string duality
• Supersymmetry of Tensionless Rotating Strings in AdS_5 x S^5, and Nearly-BPS Operators
• Slow evolution of nearly-degenerate extremal surfaces

Cited by in corpus (250)

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• Semiclassical Strings in Electric and Magnetic Fields Deformed $Ad{S}_5\times S^5$ Spacetimes
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