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129
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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Cited by 37 (6 self)
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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 of Treelevel Scattering Amplitudes
 in N=6 Superconformal ChernSimons Theory,” Phys. Rev. D 82, 045016 (2010) [arXiv:1003.6120 [hepth
"... Constraints of the osp(64) symmetry on treelevel scattering amplitudes in N = 6 superconformal Chern–Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely the four and sixpoint superamplitudes, are presented and shown to be invariant un ..."
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Cited by 32 (2 self)
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Constraints of the osp(64) symmetry on treelevel scattering amplitudes in N = 6 superconformal Chern–Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely the four and sixpoint superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory. ar X iv
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
Bipartite Field Theories: from DBrane Probes to Scattering Amplitudes
"... We introduce and initiate the investigation of a general class of 4d, N = 1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories (BFTs). BFTs underlie a wide spectrum o ..."
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Cited by 28 (4 self)
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We introduce and initiate the investigation of a general class of 4d, N = 1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories (BFTs). BFTs underlie a wide spectrum of interesting physical systems, including: D3branes probing toric CalabiYau 3folds, their mirror configurations of D6branes, cluster integrable systems in (0+1) dimensions and leading singularities in scattering amplitudes for N = 4 SYM. While our discussion is fully general, we focus on models that are relevant for scattering amplitudes. We investigate the BFT perspective on graph modifications, the emergence of CalabiYau manifolds (which arise as the master and moduli spaces of BFTs), the translation between square moves in the graph and Seiberg duality and the identification of dual theories by means of the underlying CalabiYaus, the phenomenon of loop reduction and the interpretation of the boundary operator for cells in the positive Grassmannian as higgsing in the BFT. We develop a technique based on generalized Kasteleyn matrices that permits an efficient determination of the CalabiYau geometries associated to arbitrary graphs. Our
TDuality, Dual Conformal Symmetry and Integrability for Strings on . . .
, 2009
"... In recent years two intriguing observations have been made for N = 4 super Yang–Mills theory and for superstrings on AdS5 × S 5: In the planar limit the computation of the spectrum is vastly simplified by the apparent integrability of the models. Furthermore, planar scattering amplitudes of the gaug ..."
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Cited by 15 (1 self)
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In recent years two intriguing observations have been made for N = 4 super Yang–Mills theory and for superstrings on AdS5 × S 5: In the planar limit the computation of the spectrum is vastly simplified by the apparent integrability of the models. Furthermore, planar scattering amplitudes of the gauge theory display remarkable features which have been attributed to the appearance of a dual superconformal symmetry. Here we review the connection of these two developments from the point of view of the classical symmetry by means of a superTselfduality. In particular, we show explicitly how the charges of conformal symmetry and of the integrable structure are related to the dual ones.
Dual conformal symmetry . . .
, 2009
"... We prove that 1loop npoint NMHV superamplitudes in N = 4 SYM theory are dual conformal covariant for all numbers n of external particles (after regularization and subtraction of IR divergences). This property was previously established for n ≤ 9 in arXiv:0808.0491. We derive an explicit representa ..."
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Cited by 12 (1 self)
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We prove that 1loop npoint NMHV superamplitudes in N = 4 SYM theory are dual conformal covariant for all numbers n of external particles (after regularization and subtraction of IR divergences). This property was previously established for n ≤ 9 in arXiv:0808.0491. We derive an explicit representation of these superamplitudes in terms of dual conformal crossratios. We also show that all the 1loop ‘box coefficients’ obtained from maximal cuts of N k MHV npoint functions are covariant under dual conformal transformations.