Integrable Hamiltonian for Classical Strings on AdS_5 x S^5

Abstract

We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by a 2d duality transformation. The Hamiltonian is of the Nambu type and depends on two parameters: a single S^5 angular momentum J and the string tension λ. In the general case both parameters can be finite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with λ'=λ/J^2 fixed recovers the plane-wave Hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit λ\to \infty, J fixed, the energy of short strings scales as \sqrt[4]λ while the energy of long strings scales as \sqrtλ. We further show that the gauge-fixed Hamiltonian is integrable by constructing the corresponding Lax representation. We discuss some general properties of the monodromy matrix, and verify that the asymptotic behavior of the quasi-momentum perfectly agrees with the one obtained earlier for some specific cases.

30 pages, LaTex; v2: a few comments added, misprints corrected, references added

References in corpus (21)

• Bethe Ansatz for Quantum Strings
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• On one-loop correction to energy of spinning strings in S^5
• Yang-Mills Correlation Functions from Integrable Spin Chains
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• SL(2) spin chain and spinning strings on AdS_5xS^5
• Two-loop commuting charges and the string/gauge duality
• N-Impurity Superstring Spectra Near the pp-Wave Limit
• Spin chain sigma models with fermions
• Yangian Symmetries of Matrix Models and Spin Chains: The Dilatation Operator of $\mathcal{N}$$=4$ SYM
• Bethe ansatz and fluctuations in SU(3) Yang-Mills operators
• Quantum string integrability and AdS/CFT
• The Circular, Elliptic Three Spin String from the SU(3) Spin Chain
• Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
• Spin Models and Superconformal Yang-Mills Theory
• Notes on fast moving strings
• Pulsating strings in warped AdS_6 x S^4 geometry
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• New aspects of the BMN correspondence beyond the planar limit

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