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156
Konishi operator at intermediate coupling
 J. Phys. A44
"... Abstract: TBA equations for twoparticle 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 λ ≈ 2046. The data obtained is used to analyze the properties of Yfunctions and address the issue o ..."
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Cited by 29 (1 self)
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Abstract: TBA equations for twoparticle 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 λ ≈ 2046. The data obtained is used to analyze the properties of Yfunctions 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.
A new derivation of Luscher Fterm and fluctuations around the giant magnon
 JHEP 0806 (2008) 036 [arXiv:0801.4463 [hepth
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Wrapping in maximally supersymmetric and marginally deformed N=4
 YangMills
"... In this note we give evidence for an equality of the spectra, including wrapping, of the SU(2)sector spin chain for real deformations β and β + 1/L, in marginally βdeformed N = 4 YangMills, which appears after relaxing the cyclicity constraint. Evidence for the equality is given by evaluating the ..."
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In this note we give evidence for an equality of the spectra, including wrapping, of the SU(2)sector spin chain for real deformations β and β + 1/L, in marginally βdeformed N = 4 YangMills, which appears after relaxing the cyclicity constraint. Evidence for the equality is given by evaluating the first wrapping correction to the energy of the undeformed magnon of momentum π, and the β = 1/2, physical magnon, for several spin chain lengths L. We also show that the term of maximal transcendentality coincides for both magnons to all L. As a byproduct we provide an expression for the first wrapping correction to the β = 1/2 singlemagnon operator dimension, valid for all even L. We then apply the symmetry to the magnon dispersion relation of N = 4, obtaining its first Using the techniques of integrability, much progress has been made towards confirming the complete identification of the planar spectra of N = 4 gauge theory and AdS5 × S5 string theory implied by the AdS/CFT correspondence [1]. First, the construction of the scattering matrix and the asymptotic Bethe ansatz [2, 3] turned reachable the
Nesting and dressing
"... We compute the anomalous dimensions of field strength operators Tr F L in N = 4 SYM from an asymptotic nested Bethe ansatz to allloop order. Starting from the exact solution of the oneloop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic L → ∞ limit of ..."
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We compute the anomalous dimensions of field strength operators Tr F L in N = 4 SYM from an asymptotic nested Bethe ansatz to allloop order. Starting from the exact solution of the oneloop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic L → ∞ limit of these dimensions. We also include the recently proposed phase factor for the Smatrix of the planar AdS/CFT system. The terms in the effective equation corresponding to, respectively, the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a nontrivial “filled ” structure of the theory’s BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the allloop dimension of a certain oneloop so(6) singlet state. 1 Motivation, Conclusion and Overview There is much evidence that planar N = 4 SYM theory is integrable and that its spectral problem is therefore exactly solvable. It was shown by Minahan and Zarembo that the dilatation operator in the scalar matter sector at one loop can be mapped to the Hamiltonian
Interacting finitesize magnons
 J. Phys. A41
"... We explicitly construct a large class of finitevolume twomagnon string solutions moving on × S2. In particular, by making use of the relationship between the O(3) sigma model and sineGordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breat ..."
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We explicitly construct a large class of finitevolume twomagnon string solutions moving on × S2. In particular, by making use of the relationship between the O(3) sigma model and sineGordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breatherlike solutions. After semiclassically quantizing these solutions we invert the implicit expressions for the excitation energies in certain limits and find the corrections for the multimagnon states. For the breatherlike 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
Spacetime Smatrix and Fluxtube Smatrix III. The . . .
, 2014
"... We consider lightlike Wilson loops with hexagonal geometry in the planar limit of N = 4 SuperYangMills theory. Within the OperatorProductExpansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of ..."
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We consider lightlike Wilson loops with hexagonal geometry in the planar limit of N = 4 SuperYangMills theory. Within the OperatorProductExpansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of the loops. Of particular interest are the twoparticle contributions. They comprise virtual effects like the propagation of a pair of scalars, fermions, and gluons, on top of the flux tube. Each one of them is thoroughly discussed in this paper. Our main result is the prediction of all the twist2 corrections to the expansion of the dual 6gluons MHV amplitude in the nearcollinear limit at finite coupling. At weak coupling, our result was recently used by Dixon, Drummond, Duhr and Pennington to predict the full amplitude at four loops. At strong coupling, it allows us to make contact with the classical string description and to recover the (previously elusive) AdS3 mode from the continuum of twofermion states. More generally, the twoparticle contributions serve as an exemplar for all the multiparticle corrections.
Reciprocity of gauge operators
 in N=4 SYM, arXiv:0803.3768 [hepth
, 2007
"... ABSTRACT: A recently discovered generalized GribovLipatov reciprocity holds for the anomalous dimensions of various twist operators in ��SYM. Here, we consider a class of scaling psu���operators that reduce at oneloop to twist3 maximal helicity gluonic operators. We extract from the asymptotic lo ..."
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Cited by 10 (5 self)
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ABSTRACT: A recently discovered generalized GribovLipatov reciprocity holds for the anomalous dimensions of various twist operators in ��SYM. Here, we consider a class of scaling psu���operators that reduce at oneloop to twist3 maximal helicity gluonic operators. We extract from the asymptotic longrange Bethe Ansatz a closed expression for the spin dependent anomalous dimension at four loop order and provide a complete proof of reciprocity. We comment about the interplay with possible, yet unknown, wrapping corrections.