30 research outputs found
Dressing and Wrapping
We prove that the validity of the recently proposed dressed, asymptotic Bethe
ansatz for the planar AdS/CFT system is indeed limited at weak coupling by
operator wrapping effects. This is done by comparing the Bethe ansatz
predictions for the four-loop anomalous dimension of finite-spin twist-two
operators to BFKL constraints from high-energy scattering amplitudes in N=4
gauge theory. We find disagreement, which means that the ansatz breaks down for
length-two operators at four-loop order. Our method supplies precision tools
for multiple all-loop tests of the veracity of any yet-to-be constructed set of
exact spectral equations. Finally we present a conjecture for the exact
four-loop anomalous dimension of the family of twist-two operators, which
includes the Konishi field.Comment: 20 pages, 2 tables, no figures; v2: references added, conjecture on
exact four-loop twist-two result state
Anomalous dimensions of Wilson operators in N=4 SYM theory
We present the results of two-loop calculations of the anomalous dimension matrix for the Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory for polarized and unpolarized cases. This matrix can be transformed to a triangle form by the same similarity transformation as in the leading order. The eigenvalues of the anomalous dimension matrix are expressed in terms of an universal function with its argument shifted by integer numbers. In the conclusion we discuss relations between the weak and strong coupling regimes in the framework of the AdS/CFT correspondence
Analogs of noninteger powers in general analytic QCD
In contrast to the coupling parameter in the usual perturbative QCD (pQCD),
the coupling parameter in the analytic QCD models has cuts only on the negative
semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus
reflecting correctly the analytic structure of the spacelike observables. The
Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes
the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the
pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to
evaluate in MA the physical QCD quantities whose perturbation expansion
involves noninteger powers of the pQCD coupling, a specific method of
construction of MA analogs of noninteger pQCD powers was developed by Bakulev,
Mikhailov and Stefanis (BMS). We present a construction, applicable now in any
analytic QCD model, of analytic analogs of noninteger pQCD powers; this method
generalizes the BMS approach obtained in the framework of MA. We need to know
only the discontinuity function of the analytic coupling (the analog of the
pQCD coupling) along its cut in order to obtain the analytic analogs of the
noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian)
counterparts. As an illustration, we apply the method to the evaluation of the
width for the Higgs decay into b+(bar b) pair.Comment: 29 pages, 5 figures; sections II and III extended, appendix B is ne
The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory
We present the result of a full direct component calculation for the
non-planar contribution to the four-loop anomalous dimension of the Konishi
operator in N =4 Supersymmetric Yang-Mills theory. The result contains only
zeta(5) term and is proportional to zeta(5) contribution in the planar case,
which comes purely from wrapping corrections. We have extended also our
previous calculations for the leading transcendental contribution
arXiv:0811.0607 on non-planar case and have found the same results up to a
common factor. It allows us to suggest that the non-planar contribution to the
four-loop universal anomalous dimension for the twist-2 operators with
arbitrary Lorentz spin is proportional to . This result
gives unusual double-logarithmic asymptotic for large j.Comment: 7 pages, axodraw styl
Twist-three at five loops, Bethe Ansatz and wrapping
We present a formula for the five-loop anomalous dimension of N=4 SYM
twist-three operators in the sl(2) sector. We obtain its asymptotic part from
the Bethe Ansatz and finite volume corrections from the generalized Luescher
formalism, considering scattering processes of spin chain magnons with virtual
particles that travel along the cylinder. The complete result respects the
expected large spin scaling properties and passes non-trivial tests including
reciprocity constraints. We analyze the pole structure and find agreement with
a conjectured resummation formula. In analogy with the twist-two anomalous
dimension at four-loops, wrapping effects are of order log^2 M/M^2 for large
values of the spin.Comment: 19 page
The Four-Loop Konishi in N=4 SYM
We present the result of a full direct component calculation for the planar
four-loop anomalous dimension of the Konishi operator in N =4 Supersymmetric
Yang-Mills theory. Our result confirms the results obtained from superfield
(arXiv:0712.3522, arXiv:0806.2095) and superstring (arXiv:0807.0399)
computations, which take into account finite size corrections to the all-loop
asymptotic Bethe ansatz for the integrable models describing the spectrum of
the anomalous dimensions of the gauge-invariant operators and the spectrum of
the string states in the framework of the gauge/string duality.Comment: 7 pages, some detailes of calculations adde
Six and seven loop Konishi from Luscher corrections
In the present paper we derive six and seven loop formulas for the anomalous
dimension of the Konishi operator in N=4 SYM from string theory using the
technique of Luscher corrections. We derive analytically the integrand using
the worldsheet S-matrix and evaluate the resulting integral and infinite sum
using a combination of high precision numerical integration and asymptotic
expansion. We use this high precision numerical result to fit the integer
coefficients of zeta values in the final analytical answer. The presented six
and seven loop results can be used as a cross-check with FiNLIE on the string
theory side, or with direct gauge theory computations. The seven loop level is
the theoretical limit of this Luscher approach as at eight loops
double-wrapping corrections will appear.Comment: 18 pages, typos correcte
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