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51
The AdS5 × S 5 superstring worldsheet Smatrix and crossing symmetry
, 2008
"... An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in thi ..."
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Cited by 228 (6 self)
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An Smatrix satisying the YangBaxter equation with symmetries relevant to the AdS5 × S 5 superstring has recently been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations, however due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS5 ×S 5 superstring worldsheet Smatrix. We base our construction on a Hopfalgebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the Smatrix in the generalized rapidity plane.
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
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
On the massless modes of the AdS3/CFT2 integrable systems,” arXiv:1211.1952 [hepth
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A dictionary between Roperators, onshell graphs and Yangian algebras
"... We translate between different formulations of Yangian invariants relevant for the computation of treelevel scattering amplitudes in N = 4 superYang–Mills theory. While the Roperator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally w ..."
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Cited by 5 (1 self)
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We translate between different formulations of Yangian invariants relevant for the computation of treelevel scattering amplitudes in N = 4 superYang–Mills theory. While the Roperator formulation allows to relate scattering amplitudes to structures well known from integrability, it can equally well be connected to the permutations encoded by onshell graphs. ar X iv
The WZNW model on PSU(1,12)
, 2006
"... According to the work of Berkovits, Vafa and Witten, the nonlinear sigma model on the supergroup PSU(1,12) is the essential building block for string theory on AdS3 ×S 3 ×T 4. Models associated with a nonvanishing value of the RR flux can be obtained through a psu(1,12) invariant marginal deform ..."
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Cited by 4 (1 self)
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According to the work of Berkovits, Vafa and Witten, the nonlinear sigma model on the supergroup PSU(1,12) is the essential building block for string theory on AdS3 ×S 3 ×T 4. Models associated with a nonvanishing value of the RR flux can be obtained through a psu(1,12) invariant marginal deformation of the WZNW model on PSU(1,12). We take this as a motivation to present a manifestly psu(1,12) covariant construction of the model at the WessZumino point, corresponding to a purely NSNS background 3form flux. At this point the model possesses an enhanced ̂psu(1,12) current algebra symmetry whose representation theory, including explicit character formulas, is developed systematically in the first part of the paper. The space of vertex operators and a free fermion representation for their correlation functions is our main subject in the second part. Contrary to a widespread claim, bosonic and fermionic fields are necessarily coupled to each other. The interaction changes the supersymmetry transformations, with drastic consequences for the multiplets of localized normalizable states in the model. It is only this fact which allows us to decompose the full state space into multiplets of the global supersymmetry. We analyze these decompositions systematically as a preparation for a forthcoming study of the RR deformation.
Leeuw, The RTTrealization for the deformed gl(22) Yangian
"... In this paper we work out the RTTrealization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a nonstandard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coprod ..."
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In this paper we work out the RTTrealization for the Yangian algebra of the Hubbard model and AdS/CFT correspondence. We find that this Yangian algebra is of a nonstandard type in which the levels of the Yangian mix. The crucial feature that allows this is a braiding factor that deforms the coproduct and generates the central extensions of the underlying sl(22) Lie algebra. In our RTTrealization we have also been able to incorporate the socalled secret symmetry and we were able to extend it to higher Yangian levels. Finally, we discuss the center of the Yangian and the automorphisms related to crossing symmetry. ar X iv