21 research outputs found
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
On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the
light-cone string sigma model on AdS5 x S5. We consider an evaluation
representation of the conventional Yangian built over a particular
16-dimensional long representation of the centrally extended su(2|2).
Interestingly, we find that S-matrices compatible with this evaluation
representation do not exist. On the other hand, by requiring centrally extended
su(2|2) invariance and explicitly solving the Yang-Baxter equation, we find a
scattering matrix for long-short representations of the Lie superalgebra. We
notice that this S-matrix is invariant under a different representation of
non-evaluation type, induced from the tensor product of short representations.
Our findings concern the conventional Yangian only, and are not applied to
possible algebraic extensions of the latter.Comment: Version accepted for publication in JHE
Exceptional Operators in N=4 super Yang-Mills
We consider one particularly interesting class of composite gauge-invariant
operators in N=4 super Yang-Mills theory. An exceptional feature of these
operators is that in the Thermodynamic Bethe Ansatz approach the one-loop
rapidities of the constituent magnons are shown to be exact in the 't Hooft
coupling constant. This is used to propose the mirror TBA description for these
operators. The proposal is shown to pass several non-trivial checks.Comment: 40 pages, 2 figures, 1 attached Mathematica noteboo
Quasi-local formulation of the mirror TBA
We present a method of removing all infinite sums from the various forms of
the mirror TBA equations and the energy formula of the AdS/CFT spectral
problem. This new formulation of the TBA system is quasi-local because
Y-functions that are connected by the TBA equations are at most next to nearest
neighbors with respect to the Y-system diagram of AdS/CFT.Comment: 13 pages, LaTe
Scattering of Giant Magnons in CP^3
We study classical scattering phase of CP^2 dyonic giant magnons in R_t x
CP^3. We construct two-soliton solutions explicitly by the dressing method.
Using these solutions, we compute the classical time delays for the scattering
of giant magnons, and compare them to boundstate S-matrix elements derived from
the conjectured AdS_4/CFT_3 S-matrix by Ahn and Nepomechie in the strong
coupling limit. Our result is consistent with the conjectured S-matrix. The
dyonic solutions play an essential role in revealing the polarization
dependence of scattering phase.Comment: 29 pages; v2: minor corrections; v3: minor corrections, references
added ; v4: minor corrections ; v5: minor corrections based on the published
versio
Twist-two operators and the BFKL regime — nonstandard solutions of the Baxter equation
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
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
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