21 research outputs found
Finite-size effects in the superconformal beta-deformed N=4 SYM
We study finite size effects for composite operators in the SU(2) sector of
the superconformal beta-deformed N=4 SYM theory. In particular we concentrate
on the spectrum of one single magnon. Since in this theory one-impurity states
are non BPS we compute their anomalous dimensions including wrapping
contributions up to four loops and discuss higher order effects.Comment: LaTeX, mpost, feynmf, 20 pages, 4 figures, 5 tables; v2: references
added, equations (4.13) and (4.17) correcte
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
Wrapping at four loops in N=4 SYM
We present the planar four-loop anomalous dimension of the composite operator
tr(phi[Z,phi]Z) in the flavour SU(2) sector of the N=4 SYM theory. At this loop
order wrapping interactions are present: they give rise to contributions
proportional to zeta(5) increasing the level of transcendentality of the
anomalous dimension. In a sequel of this paper all the details of our
calculation will be reported.Comment: LaTeX, 10 pages, 1 table; v2: sign changed in W_1 of Fig.1 and
corresponding correction for the coeff. of zeta(3) in the final result,
references added; v3: version published in Phys.Lett.
Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
We study the spectrum of one single magnon in the superconformal
beta-deformed N=4 SYM theory in the planar limit. We compute the anomalous
dimensions of one-impurity operators O_{1,L}= tr(phi Z^{L-1}), including
wrapping contributions at their critical order L.Comment: LaTeX, feynmf, Metapost, 20 pages, 11 figures, v2: results up to 11
loops completed, appendix on integral calculation extende
Konishi operator at intermediate coupling
TBA equations for two-particle states from the sl(2) sector proposed by
Arutyunov, Suzuki and the author are solved numerically for the Konishi
operator descendent up to 't Hooft's coupling lambda ~ 2046. The data obtained
is used to analyze the properties of Y-functions and address the issue of the
existence of the critical values of the coupling. In addition we find a new
integral representation for the BES dressing phase which substantially reduces
the computational time.Comment: lots of figures, v2: improved numerics, c1=2, c2=0, c4 does not
vanis
Interacting finite-size magnons
We explicitly construct a large class of finite-volume two-magnon string
solutions moving on R x S^2. In particular, by making use of the relationship
between the O(3) sigma model and sine-Gordon theory we are able to find
solutions corresponding to the periodic analogues of magnon scattering and
breather-like solutions. After semi-classically quantizing these solutions we
invert the implicit expressions for the excitation energies in certain limits
and find the corrections for the multi-magnon states. For the breather-like
solutions we express the energies directly in terms of the action variable
whereas for the scattering solution we express the result as a combination of
corrections to the dispersion relation and to the scattering phase.Comment: 45pages, 7figures, v2: simplified expressions for periods and angular
momenta when elliptic modulus is greater than one, references added, typos
correcte
Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
We review the construction of the AdS/CFT dressing factor, its analytic
properties and several checks of its validity.Comment: 22 pages, see also overview article arXiv:1012.3982, v2: references
to other chapters update
Anomalous dimension with wrapping at four loops in N=4 SYM
In this paper we give all the details of the calculation that we presented in our previous paper arXiv:0712.3522, concerning the four-loop anomalous dimension of the Konishi descendant tr(\phi Z\phi Z-\phi \phi Z Z) in the SU(2) sector of the N=4 planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an N=1 superspace approach and Gegenbauer polynomial x-space techniques