83 research outputs found
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
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
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
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.
Orbifolded Konishi from the Mirror TBA
Starting with a discussion of the general applicability of the simplified
mirror TBA equations to simple deformations of the AdS_5 x S^5 superstring, we
proceed to study a specific type of orbifold to which the undeformed simplified
TBA equations directly apply. We then use this set of equations, as well as
Luscher's approach, to determine the NLO wrapping correction to the energy of
what we call the orbifolded Konishi state, and show that they perfectly agree.
In addition we discuss wrapping corrections to the ground state energy of the
orbifolded model under consideration.Comment: 26 pages, 5 figures, v2: corrected typos, added a short discussion on
the ground state of the model; as submitted to J. Phys.
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
Supergraphs and the cubic Leigh-Strassler model
We discuss supergraphs and their relation to "chiral functions" in N=4 Super
Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop
result of Sieg's we make an all loop conjecture for the rational contributions
of certain classes of supergraphs. We then apply superspace techniques to the
"cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that
there are order 2^L/L single trace operators of length L which have zero
anomalous dimensions to all loop order in the planar limit. We then compute the
anomalous dimensions for another class of single trace operators we call
one-pair states. Using the conjecture we can find a simple expression for the
rational part of the anomalous dimension which we argue is valid at least up to
and including five-loop order. Based on an explicit computation we can compute
the anomalous dimension for these operators to four loops.Comment: 22 pages; v2: Conjecture modified to apply only for the rational part
of the chiral functions. Typos fixed. Minor modification
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
Four-loop anomalous dimensions in Leigh-Strassler deformations
We determine the scalar part of the four-loop chiral dilatation operator for
Leigh-Strassler deformations of N=4 super Yang-Mills. This is sufficient to
find the four-loop anomalous dimensions for operators in closed scalar
subsectors. This includes the SU(2) subsector of the (complex)
beta-deformation, where we explicitly compute the anomalous dimension for
operators with a single impurity. It also includes the "3-string null"
operators of the cubic Leigh-Strassler deformation. Our four-loop results show
that the rational part of the anomalous dimension is consistent with a
conjecture made in arXiv:1108.1583 based on the three-loop result of
arXiv:1008.3351 and the N=4 magnon dispersion relation. Here we find additional
zeta(3) terms.Comment: Latex, feynmp, 21 page
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