SL(2) spin chain and spinning strings on AdS_5xS^5

Abstract

We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL(2,R). By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL(2,R)/U(1). The same sigma model is found by considering strings rotating with large angular momentum in AdS_5xS^5. The spinning strings are identified with semiclassical coherent states built out of SL(2,R) spin chain states.

18 pages, 1 fig, References added. Earlier results in [38] are pointed out

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• Spinning strings and AdS/CFT duality
• Integrability in QCD and beyond
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• From Free Fields to $AdS$ -- III
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• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
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• Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons
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• Wound and Rotating Strings in AdS_5 x S^5
• "Massive" Higher Spin Multiplets and Holography
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
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• Non-compact quantum spin chains as integrable stochastic particle processes
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• String theories on warped AdS backgrounds and integrable deformations of spin chains
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• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
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• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
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• Giant Magnons under NS-NS and Melvin Fields
• Multi-spin String Solutions in Magnetic-flux Deformed $Ad{S}_n\times S^m$ Spacetime
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• Spin chain from membrane and the Neumann-Rosochatius integrable system
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• Spin chain from marginally deformed AdS_3 x S^3
• 2D Heisenberg model from rotating membrane
• From Baxter Q-Operators to Local Charges
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• The $\mathrm{SL}(2,\mathbb{R})$ Wess-Zumino-Novikov-Witten spin-chain $\sigma$-model
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