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132
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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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
The hexagon Wilson loop and the BDS ansatz for the sixgluon amplitude, Phys
 Lett. B
"... As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal lightlike Wilson loop at two loops in N = 4 super YangMills theory. We compare its finite part to the BernDixonSmirnov (BDS) conjecture for the finite part of the sixgluon amplitude. We find that the two e ..."
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Cited by 75 (12 self)
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As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal lightlike Wilson loop at two loops in N = 4 super YangMills theory. We compare its finite part to the BernDixonSmirnov (BDS) conjecture for the finite part of the sixgluon amplitude. We find that the two expressions have the same behavior in the collinear limit, but they differ by a nontrivial function of the three (dual) conformally invariant variables. This implies that either the BDS conjecture or the gluon amplitude/Wilson loop duality fails for the sixgluon amplitude, starting from two loops. Our results are in qualitative agreement with the analysis of Alday and Maldacena of scattering amplitudes with infinitely many external gluons. 1 UMR 5108 associée à l’Université de Savoie
Hexagon Wilson loop = sixgluon MHV amplitude
, 2008
"... We compare the twoloop corrections to the finite part of the lightlike hexagon Wilson loop with the recent numerical results for the finite part of the MHV sixgluon amplitude in N = 4 SYM theory by Bern, Dixon, Kosower, Roiban, Spradlin, Vergu and Volovich (arXiv:0803.1465 [hepth]) and demonstra ..."
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Cited by 45 (5 self)
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We compare the twoloop corrections to the finite part of the lightlike hexagon Wilson loop with the recent numerical results for the finite part of the MHV sixgluon amplitude in N = 4 SYM theory by Bern, Dixon, Kosower, Roiban, Spradlin, Vergu and Volovich (arXiv:0803.1465 [hepth]) and demonstrate that they coincide within the error bars and, at the same time, they differ from the BDS ansatz by a nontrivial function of (dual) conformal kinematical invariants. This provides strong evidence that the Wilson loop/scattering amplitude duality holds in planar N = 4 SYM theory to all loops for an arbitrary number of external particles.
Bootstrapping the threeloop hexagon
"... We consider the hexagonal Wilson loop dual to the sixpoint MHV amplitude in planar N = 4 super YangMills theory. We apply constraints from the operator product expansion in the nearcollinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natu ..."
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We consider the hexagonal Wilson loop dual to the sixpoint MHV amplitude in planar N = 4 super YangMills theory. We apply constraints from the operator product expansion in the nearcollinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol’s entries, we determine the symbol up to just two undetermined constants. In the multiRegge limit, both constants drop out from the symbol, enabling us to make a nontrivial confirmation of the BFKL prediction for the leadinglog approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full threeloop remainder function in the multiRegge limit, beyond the leadinglog approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an allloop prediction for the real part of the remainder function in multiRegge 3 → 3 scattering. In the multiRegge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic sixpoint kinematics other functions are required.
Analytic result for the twoloop sixpoint NMHV amplitude in N = 4 super YangMills theory
"... We provide a simple analytic formula for the twoloop sixpoint ratio function of planar N = 4 super YangMills theory. This result extends the analytic knowledge of multiloop sixpoint amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant ..."
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Cited by 33 (5 self)
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We provide a simple analytic formula for the twoloop sixpoint ratio function of planar N = 4 super YangMills theory. This result extends the analytic knowledge of multiloop sixpoint amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the twoloop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for lightlike (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal crossratios, plus precisely two functions that are not of this type. One of the functions, the loop integral Ω (2), also plays a key role in a new representation of
Symmetries and analytic properties of scattering amplitudes
 in N=4 SYM theory
"... In addition to the superconformal symmetry of the underlying Lagrangian, the scattering amplitudes in planar N = 4 superYangMills theory exhibit a new, dual superconformal symmetry. We address the question of how powerful these symmetries are to completely determine the scattering amplitudes. We u ..."
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Cited by 29 (2 self)
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In addition to the superconformal symmetry of the underlying Lagrangian, the scattering amplitudes in planar N = 4 superYangMills theory exhibit a new, dual superconformal symmetry. We address the question of how powerful these symmetries are to completely determine the scattering amplitudes. We use the example of the NMHV superamplitudes to show that the combined action of conventional and dual superconformal symmetries is not sufficient to fix all the freedom in the treelevel amplitudes. We argue that the additional information needed comes from the study of the analytic properties of the amplitudes. The requirement of absence of spurious singularities, together with the correct multiparticle singular behavior, determines the unique linear combination of superinvariants corresponding to the n−particle NMHV superamplitude. The same result can be obtained recursively, by relating the n − and (n − 1)−particle amplitudes in the singular collinear limit. We also formulate constraints on the loop corrections to the superamplitudes, following from the analytic behavior in the above limits. We then show that, at oneloop level, the holomorphic anomaly of the tree amplitudes leads to the breakdown of dual Poincaré supersymmetry (equivalent to ordinary special conformal supersymmetry) of the ratio of the NMHV and MHV superamplitudes, but this anomaly does not affect dual conformal symmetry. 1
Analyticity for MultiRegge Limits of the BernDixonSmirnov Amplitudes
, 2009
"... As a consequence of the AdS/CFT correspondence, planar N = 4 super YangMills SU(N) theory is expected to exhibit stringy behavior and multiRegge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flat ..."
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Cited by 21 (8 self)
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As a consequence of the AdS/CFT correspondence, planar N = 4 super YangMills SU(N) theory is expected to exhibit stringy behavior and multiRegge asymptotic. In this paper we extend our recent investigation to consider issues of analyticity, a central feature of Regge asymptotics. We contrast flatspace open string theory with the N = 4 theory, as represented by the BDS conjecture for ngluon scattering [1], believed to be exact for n = 4,5 and modified only by a function of crossratios for n ≥ 6. We present several examples where the two theories differ (sometimes dramatically). It is suggested that the differences are due to the necessity for an IR regulator for the trajectories of N = 4 SYM conformal theory in contrast to that of flat space open string which has an intrinsic mass scale and linear trajectories. We point out the breakdown of Steinmann rules under the BDS ansatz (with no O(ǫ) terms in the exponent) and emphasize that, in spite of this difficulty, factorization is still realized in the multiRegge region [2]. This suggests that the O(ǫ) contributions in the exponent of BDS amplitudes are crucial to the