Integrable Hamiltonian for Classical Strings on AdS5 x S5

By G. Arutyunov, S. Frolov. 2004

215 citations recorded by the source corpus.

We flnd the hamiltonian for physical excitations of the classical bosonic string propagating in the AdS5£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 ‚. In the general case both parameters can be flnite. The space of string states consists of short and long strings. In the sector of short strings the large J expansion with ‚ 0 = ‚=J 2 flxed recovers the plane-wave hamiltonian and higher-order corrections recently studied in the literature. In the strong coupling limit ‚ ! 1, J flxed, the energy of short strings scales as 4 p ‚ while the energy of long strings scales as p ‚. We further show that the gauge-flxed 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 speciflc cases.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a021af5de89cac16f0fa071500e8b6ca013ce1a2

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Citations in the corpus

On string S-matrix, bound states and TBA (2007, methodology): “The gauge-fixed Lagrangian in the generalized a-gauge can be obtained either from the corresponding Hamiltonian [59, 57] by using the canonical formalism or by T-dualizing the action in the direction canonically conjugate to the light-cone momentum P+ [26].”
Lax pair for strings in Lunin-Maldacena background (2005, methodology): “The The gauge transformation is similar to the one used in [42] to derive a local and periodic Lax connection for the Hamiltonian of strings on AdS5 × S .”
Planar N = 4 gauge theory and the Hubbard model (2005, background): “Some progress has also been made towards deriving quantum integrability directly from the string sigma model [ 49 ].”
String hypothesis for the AdS5 × S5 mirror (2009, methodology): “One starts by imposing the lightcone gauge for the AdS5 × S superstring, and obtains a 2-d non-linear sigma model defined on a cylinder of circumference equal to the light-cone momentum P+ [6, 7].”
Wrapping interactions and a new source of corrections to the spin-chain/string duality (2005, background): “(10) For the world sheet string theories in curved AdS space-time it was pointed out [40, 14, 16, 9] that the usual light cone gauge like τ = t (where t is e.”
Gauge-string duality for superconformal deformations of N=4 super Yang-Mills theory (2005, unknown): “10) Rα = MAα M−1 − M ∂αM = Âα + i 2 (∂α ̃̃ φ2 − ∂α ̃̃ φ1) σ3 , (27)A similar idea was used in [67] to derive a local and periodic Lax connection for the Hamiltonian of strings on AdS5 × S(5) .”
The Algebraic Curve of Classical Superstrings on AdS5×S5 (2005, background): “Likewise, the involved group manifolds are considered to be universal coverings.”
Spinning strings in AdS5 × S5: one-loop correction to energy in SL(2) sector (2005, unknown): “semiclassical states at the two leading orders in � is based on directly relating the thermodynamic limit of the Bethe ansatz equations to the integral equation representing the general integrability-based solution of the corresponding sector of the classical AdS5 × S5 sigma model [13, 28, 39, 40, ”
The AdS 5 ×S 5 superstring worldsheet S matrix and crossing symmetry (2006, methodology): “One of the most fascinating discoveries in recent years was the unravelling of integrable structures in planar N = 4 SYM [1, 2, 3, 4] and in superstring theory on AdS5 × S(5) [5, 6, 7, 8, 9, 10, 11].”
Towards integrability for AdS 3 / CFT 2 ?> (2014, background): “In a more general a-dependent gauge fixing [91, 203, 204], we would have ` = P+ = aE t.”
The factorized S-matrix of CFT/AdS (2004, methodology): “Very recently, the Hamiltonian of the classical bosonic string propagating on AdS5 × S was shown to be integrable by constructing, in a special gauge, the corresponding Lax representation [11].”