103 research outputs found
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
Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
The result for the six-loop anomalous dimension of twist-three operators in
the planar N=4 SYM theory is presented. The calculations were performed along
the paper arXiv:0912.1624. This result provides a new data for testing the
proposed spectral equations for planar AdS/CFT correspondence.Comment: 19 pages, typos corrected, details adde
Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
We consider N=4 SYM and a class of spin N, length-3, twist operators beyond
the well studied sl(2) subsector. They can be identified at one-loop with three
gluon operators. At strong coupling, they are associated with spinning strings
with two spins in AdS5. We exploit the Y-system to compute the leading
weak-coupling four loop wrapping correction to their anomalous dimension. The
result is written in closed form as a function of the spin N. We combine the
wrapping correction with the known four-loop asymptotic Bethe Ansatz
contribution and analyze special limits in the spin N. In particular, at large
N, we prove that a generalized Gribov-Lipatov reciprocity holds. At negative
unphysical spin, we present a simple BFKL-like equation predicting the
rightmost leading poles.Comment: 18 page
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
Five-loop anomalous dimension at critical wrapping order in N=4 SYM
We compute the anomalous dimension of a length-five operator at five-loop
order in the SU(2) sector of N=4 SYM theory in the planar limit. This is
critical wrapping order at five loops. The result is obtained perturbatively by
means of N=1 superspace techniques. Our result from perturbation theory
confirms explicitly the formula conjectured in arXiv:0901.4864 for the
five-loop anomalous dimension of twist-three operators. We also explicitly
obtain the same result by employing the recently proposed Y-system.Comment: LaTeX, feynmp, 34 pages, 21 figures, 8 table
Double-logs, Gribov-Lipatov reciprocity and wrapping
We study analytical properties of the five-loop anomalous dimension of
twist-2 operators at negative even values of Lorentz spin. Following L. N.
Lipatov and A. I. Onishchenko, we have found two possible generalizations of
double-logarithmic equation, which allow to predict a lot of poles of anomalous
dimension of twist-2 operators at all orders of perturbative theory from the
known results. Second generalization is related with the reciprocity-respecting
function, which is a single-logarithmic function in this case. We have found,
that the knowledge of first orders of the reciprocity-respecting function gives
all-loop predictions for the highest poles. Obtained predictions can be used
for the reconstruction of a general form of the wrapping corrections for
twist-2 operators.Comment: 17 pages, references adde
Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
We apply the recently proposed quantum spectral curve technique to the study
of twist operators in planar N=4 SYM theory. We focus on the small spin
expansion of anomalous dimensions in the sl(2) sector and compute its first two
orders exactly for any value of the 't Hooft coupling. At leading order in the
spin S we reproduced Basso's slope function. The next term of order S^2
structurally resembles the Beisert-Eden-Staudacher dressing phase and takes
into account wrapping contributions. This expansion contains rich information
about the spectrum of local operators at strong coupling. In particular, we
found a new coefficient in the strong coupling expansion of the Konishi
operator dimension and confirmed several previously known terms. We also
obtained several new orders of the strong coupling expansion of the BFKL
pomeron intercept. As a by-product we formulated a prescription for the correct
analytical continuation in S which opens a way for deriving the BFKL regime of
twist two anomalous dimensions from AdS/CFT integrability.Comment: 53 pages, references added; v3: due to a typo in the coefficients C_2
and D_2 on page 29 we corrected the rational part of the strong coupling
predictions in equations (1.5-6), (6.22-24), (6.27-30) and in Table
Quantum folded string and integrability: from finite size effects to Konishi dimension
Using the algebraic curve approach we one-loop quantize the folded string
solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit
result valid for arbitrary values of its Lorentz spin S and R-charge J in terms
of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and
derive the leading three coefficients of strong coupling expansion of short
operators. Notably, our result evaluated for the anomalous dimension of the
Konishi state gives 2\lambda^{1/4}-4+2/\lambda^{1/4}. This reproduces correctly
the values predicted numerically in arXiv:0906.4240. Furthermore we compare our
result using some new numerical data from the Y-system for another similar
state. We also revisited some of the large S computations using our methods. In
particular, we derive finite--size corrections to the anomalous dimension of
operators with small J in this limit.Comment: 20 pages, 1 figure; v2: references added, typos corrected; v3: major
improvement of the references; v4: Discussion of short operators is
restricted to the case n=1. This restriction does not affect the main results
of the pape
Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
We revisit the computation of the 2-loop correction to the energy of a folded
spinning string in AdS_5 with an angular momentum J in S^5 in the scaling limit
log S, J >>1 with J / log S fixed. This correction gives the third term in the
strong-coupling expansion of the generalized scaling function. The computation,
using the AdS light-cone gauge approach developed in our previous paper, is
done by expanding the AdS_5 x S^5 superstring partition function near the
generalized null cusp world surface associated to the spinning string solution.
The result corrects and extends the previous conformal gauge result of
arXiv:0712.2479 and is found to be in complete agreement with the corresponding
terms in the generalized scaling function as obtained from the asymptotic Bethe
ansatz in arXiv:0805.4615 (and also partially from the quantum O(6) model and
the Bethe ansatz data in arXiv:0809.4952). This provides a highly nontrivial
strong coupling comparison of the Bethe ansatz proposal with the quantum AdS_5
x S^5 superstring theory, which goes beyond the leading semiclassical term
effectively controlled by the underlying algebraic curve. The 2-loop
computation we perform involves all the structures in the AdS light-cone gauge
superstring action of hep-th/0009171 and thus tests its ultraviolet finiteness
and, through the agreement with the Bethe ansatz, its quantum integrability. We
do most of the computations for a generalized spinning string solution or the
corresponding null cusp surface that involves both the orbital momentum and the
winding in a large circle of S^5.Comment: 50 pages, late
Spinning strings and integrable spin chains in the AdS/CFT correspondence
In this introductory review we discuss dynamical tests of the AdS_5 x S^5
string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we
argue that semiclassical string energies yield information on the quantum
spectrum of the string in the limit of large angular momenta on the S^5. The
energies of the folded and circular spinning string solutions rotating on a S^3
within the S^5 are derived, which yield all loop predictions for the dual gauge
theory scaling dimensions. These follow from the eigenvalues of the dilatation
operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display
its reformulation in terms of a Heisenberg s=1/2 spin chain along with the
coordinate Bethe ansatz for its explicit diagonalization. In order to make
contact to the spinning string energies we then study the thermodynamic limit
of the one-loop gauge theory Bethe equations and demonstrate the matching with
the folded and closed string result at this loop order. Finally the known gauge
theory results at higher-loop orders are reviewed and the associated long-range
spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop
conjecture for the gauge theory Bethe equations. This uncovers discrepancies at
the three-loop order between gauge theory scaling dimensions and string theory
energies and the implications of this are discussed. Along the way we comment
on further developments and generalizations of the subject and point to the
relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2:
improvements in the text and references adde
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