541 research outputs found
On Hamiltonian structure of the spin Ruijsenaars-Schneider model
The Hamiltonian structure of spin generalization of the rational
Ruijsenaars-Schneider model is found by using the Hamiltonian reduction
technique. It is shown that the model possesses the current algebra symmetry.
The possibility of generalizing the found Poisson structure to the
trigonometric case is discussed and degeneration to the Euler-Calogero-Moser
system is examined.Comment: latex, 16 pages, references are adde
The Bajnok-Janik formula and wrapping corrections
We write down the simplified TBA equations of the string
sigma-model for minimal energy twist-two operators in the sl(2) sector of the
model. By using the linearized version of these TBA equations it is shown that
the wrapping corrected Bethe equations for these states are identical, up to
O(g^8), to the Bethe equations calculated in the generalized L\"uscher approach
(Bajnok-Janik formula). Applications of the Bajnok-Janik formula to
relativistic integrable models, the nonlinear O(n) sigma models for n=2,3,4 and
the SU(n) principal sigma models, are also discussed.Comment: Latex, 22 pages, published versio
Quantum corrections to the string Bethe ansatz
One-loop corrections to the energy of semiclassical rotating strings contain
both analytic and non-analytic terms in the 't Hooft coupling. Analytic
contributions agree with the prediction from the string Bethe ansatz based on
the classical S-matrix, but in order to include non-analytic contributions
quantum corrections are required. We find a general expression for the first
quantum correction to the string Bethe ansatz.Comment: 12 pages. Latex. v2: Misprints corrected and references adde
Worldsheet Scattering in AdS_5 x S^5
We calculate the S-matrix in the gauge-fixed sigma-model on AdS_5 x S^5 to
the leading order in perturbation theory, and analyze how supersymmetry is
realized on the scattering states. A mild nonlocality of the supercharges
implies that their action on multi-particle states does not follow the Leibniz
rule, which is replaced by a nontrivial coproduct. The plane wave symmetry
algebra is thus naturally enhanced to a Hopf algebra. The scattering matrix
elements obey the classical Yang-Baxter equation modified by the existence of
the coproduct. This structure mirrors that of the large 't Hooft coupling
expansion of the S-matrix for the spin chain in the dual super-Yang-Mills
theory.Comment: 51 pages, v2: references added, v3: sign in (2.12), (6.19) and (6.21)
corrected; v4: discussion of classical YBE is considerably modifie
On correlation functions of operators dual to classical spinning string states
We explore how to compute, classically at strong coupling, correlation
functions of local operators corresponding to classical spinning string states.
The picture we obtain is of `fattened' Witten diagrams, the evaluation of which
turns out to be surprisingly subtle and requires a modification of the naive
classical action due to a necessary projection onto appropriate wave functions.
We examine string solutions which compute the simplest case of a two-point
function and reproduce the right scaling with the anomalous dimensions
corresponding to the energies of the associated spinning string solutions. We
also describe, under some simplifying assumptions, how the spacetime dependence
of a conformal three-point correlation function arises in this setup.Comment: 27 pages, 3 figures; v2: references and comments added
On Integrability of Classical SuperStrings in AdS_5 x S^5
We explore integrability properties of superstring equations of motion in
AdS_5 x S^5. We impose light-cone kappa-symmetry and reparametrization gauges
and construct a Lax representation for the corresponding Hamiltonian dynamics
on subspace of physical superstring degrees of freedom. We present some
explicit results for the corresponding conserved charges by consistently
reducing the dynamics to AdS_3 x S^3 and AdS_3 x S^1 subsectors containing both
bosonic and fermionic fields.Comment: JHEP style, 32 pages; v2: refined discussion of monodromy, refs adde
The algebra of flat currents for the string on AdS_5 x S^5 in the light-cone gauge
We continue the program initiated in hep-th/0411200 and calculate the algebra
of the flat currents for the string on AdS_5 x S^5 background in the light-cone
gauge with kappa-symmetry fixed. We find that the algebra has a closed form and
that the non-ultralocal terms come with a weight factor e^{\phi} that depends
on the radial AdS_5 coordinate. Based on results in two-dimensional sigma
models coupled to gravity via the dilaton field, this suggests that the algebra
of transition matrices in the present case is likely to be unambigous.Comment: 27 pages, references added, version published in JHE
Asymptotic Bethe equations for open boundaries in planar AdS/CFT
We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries
scattering theory describing the excitations of a free open string propagating
in , carrying large angular momentum , and ending on
a maximal giant graviton whose angular momentum is in the same plane. We thus
obtain the all-loop Bethe equations describing the spectrum, for finite but
large, of the energies of such strings, or equivalently, on the gauge side of
the AdS/CFT correspondence, the anomalous dimensions of certain operators built
using the epsilon tensor of SU(N). We also give the Bethe equations for strings
ending on a probe D7-brane, corresponding to meson-like operators in an
gauge theory with fundamental matter.Comment: 30 pages. v2: minor changes and discussion section added, J.Phys.A
version
Hybrid-NLIE for the AdS/CFT spectral problem
Hybrid-NLIE equations, an alternative finite NLIE description for the
spectral problem of the super sigma model of AdS/CFT and its gamma-deformations
are derived by replacing the semi-infinite SU(2) and SU(4) parts of the AdS/CFT
TBA equations by a few appropriately chosen complex NLIE variables, which are
coupled among themselves and to the Y-functions associated to the remaining
central nodes of the TBA diagram. The integral equations are written explicitly
for the ground state of the gamma-deformed system. We linearize these NLIE
equations, analytically calculate the first correction to the asymptotic
solution and find agreement with analogous results coming from the original TBA
formalism. Our equations differ substantially from the recently published
finite FiNLIE formulation of the spectral problem.Comment: 63 pages, 1 figur
A numerical test of the Y-system in the small size limit of the SU(2)x SU(2) Principal Chiral Model
Recently, Kazakov, Gromov and Vieira applied the discrete Hirota dynamics to
study the finite size spectra of integrable two dimensional quantum field
theories. The method has been tested from large values of the size L down to
moderate values using the SU(2) x SU(2) principal chiral model as a theoretical
laboratory. We continue the numerical analysis of the proposed non-linear
integral equations showing that the deep ultraviolet region L -> 0 is
numerically accessible. To this aim, we introduce a relaxed iterative algorithm
for the numerical computation of the low-lying part of the spectrum in the U(1)
sector. We discuss in details the systematic errors involved in the
computation. When a comparison is possible, full agreement is found with
previous TBA computations.Comment: 28 pages, 24 figure
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