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86
Yangian symmetry of scattering amplitudes
 in N = 4 super YangMills theory,” arXiv:0902.2987 [hepth
"... Treelevel scattering amplitudes in N = 4 super YangMills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,24) of the theory. In this paper we derive the action ..."
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Cited by 129 (15 self)
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Treelevel scattering amplitudes in N = 4 super YangMills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,24) of the theory. In this paper we derive the action of the dual superconformal generators in onshell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,24) symmetry algebra to a Yangian. The nonlocal Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,24). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is The N = 4 supersymmetric YangMills theory (SYM) [1] is a remarkable model of mathematical physics. To begin with it is the gauge theory with maximal supersymmetry and it is superconformally invariant at the classical and quantum level with a coupling constant free of
Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
, 2009
"... Moving from the mirror theory BetheYang equations proposed by Arutynov and Frolov, we derive the Thermodynamic Bethe Ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Ysystem) satisfied by the exponentia ..."
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Cited by 127 (5 self)
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Moving from the mirror theory BetheYang equations proposed by Arutynov and Frolov, we derive the Thermodynamic Bethe Ansatz equations which should control the spectrum of the planar AdS5/CFT4 correspondence. The associated set of universal functional relations (Ysystem) satisfied by the exponentials of the TBA pseudoenergies is deduced, confirming the structure inferred by Gromov, Kazakov and Vieira.
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
qdeformed supersymmetry and dynamic magnon representations,” arXiv:0704.2069 [hepth
"... It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J an ..."
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Cited by 13 (2 self)
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It was recently noted that the dispersion relation for the magnons of planar N = 4 SYM can be identified with the Casimir of a certain deformation of the Poincaré algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(22) ⋉ R 2, we derive a qdeformed superPoincaré symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed restframe representation. We comment on aspects of the coalgebra structure and some implications for the question of boostcovariance of the Smatrix. 1 1
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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Cited by 12 (0 self)
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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.
Leading singularities and offshell conformal integrals, JHEP 1308
, 2013
"... Abstract The threeloop fourpoint function of stresstensor multiplets in N = 4 super YangMills theory contains two so far unknown, offshell, conformal integrals, in addition to the known, laddertype integrals. In this paper we evaluate the unknown integrals, thus obtaining the threeloop corre ..."
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Cited by 9 (0 self)
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Abstract The threeloop fourpoint function of stresstensor multiplets in N = 4 super YangMills theory contains two so far unknown, offshell, conformal integrals, in addition to the known, laddertype integrals. In this paper we evaluate the unknown integrals, thus obtaining the threeloop correlation function analytically. The integrals have the generic structure of rational functions multiplied by (multiple) polylogarithms. We use the idea of leading singularities to obtain the rational coefficients, the symbol with an appropriate ansatz for its structure as a means of characterising multiple polylogarithms, and the technique of asymptotic expansion of Feynman integrals to obtain the integrals in certain limits. The limiting behaviour uniquely fixes the symbols of the integrals, which we then lift to find the corresponding polylogarithmic functions. The final formulae are numerically confirmed. The techniques we develop can be applied more generally, and we illustrate this by analytically evaluating one of the integrals contributing to the same fourpoint function at four loops. This example shows a connection between the leading singularities and the entries of the symbol. In memory of Francis Dolan.
Finitesize Effects for Single Spike
 JHEP
, 2008
"... We use the reduction of the string dynamics on Rt × S 3 to the NeumannRosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sineGordon integrable model. This mapping relates the parameters in the solutions on both sides of the co ..."
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We use the reduction of the string dynamics on Rt × S 3 to the NeumannRosochatius integrable system to map all string solutions described by this dynamical system onto solutions of the complex sineGordon integrable model. This mapping relates the parameters in the solutions on both sides of the correspondence. In the framework of this approach, we find finitesize string solutions, their images in the (complex) sineGordon system, and the leading finitesize effects of the single spike “E − ∆ϕ ” relation for both Rt × S 2 and Rt × S 3 cases. On leave from Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences,