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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
Recursion relations for gauge theory amplitudes with massive particles
"... Preprint typeset in JHEP style PAPER VERSION hepth/0507161 ..."
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Cited by 51 (7 self)
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Preprint typeset in JHEP style PAPER VERSION hepth/0507161
A recursion relation for gravity amplitudes
 NUCL. PHYS. B
, 2005
"... Britto, Cachazo and Feng have recently derived a recursion relation for treelevel scattering amplitudes in YangMills. This relation has a bilinear structure inherited from factorisation on multiparticle poles of the scattering amplitudes – a rather generic feature of field theory. Motivated by th ..."
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Cited by 43 (8 self)
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Britto, Cachazo and Feng have recently derived a recursion relation for treelevel scattering amplitudes in YangMills. This relation has a bilinear structure inherited from factorisation on multiparticle poles of the scattering amplitudes – a rather generic feature of field theory. Motivated by this, we propose a new recursion relation for scattering amplitudes of gravitons at tree level. Using this recursion relation, we derive a new general formula for the MHV treelevel scattering amplitude for n gravitons. Finally, we comment on the existence of recursion relations in general field theories.
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
From Trees to Loops and Back
, 2008
"... We argue that generic oneloop scattering amplitudes in supersymmetric YangMills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of oneloop nonMHV amplitudes obtained from MHV diagrams. This proof relies only on ..."
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Cited by 27 (8 self)
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We argue that generic oneloop scattering amplitudes in supersymmetric YangMills theories can be computed equivalently with MHV diagrams or with Feynman diagrams. We first present a general proof of the covariance of oneloop nonMHV amplitudes obtained from MHV diagrams. This proof relies only on the local character in Minkowski space of MHV vertices and on an application of the Feynman Tree Theorem. We then show that the discontinuities of oneloop scattering amplitudes computed with MHV diagrams are precisely the same as those computed with standard methods. Furthermore, we analyse collinear limits and soft limits of generic nonMHV amplitudes in supersymmetric YangMills theories with oneloop MHV diagrams. In particular, we find a simple explicit derivation of the universal oneloop splitting functions in supersymmetric YangMills theories to all orders in the dimensional regularisation parameter, which is in complete agreement with known results. Finally, we present concrete and illustrative applications of Feynman’s Tree Theorem to oneloop MHV diagrams as well as to oneloop Feynman diagrams.
Loop Amplitudes in Pure YangMills From Generalised Unitarity
, 2005
"... We show how generalised unitarity cuts in D = 4 − 2ǫ dimensions can be used to calculate efficiently complete oneloop scattering amplitudes in nonsupersymmetric YangMills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cutconstructible parts. We tes ..."
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Cited by 26 (5 self)
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We show how generalised unitarity cuts in D = 4 − 2ǫ dimensions can be used to calculate efficiently complete oneloop scattering amplitudes in nonsupersymmetric YangMills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cutconstructible parts. We test the validity of our method by rederiving the oneloop ++++, −+++, −−++, −+−+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.