Abstract
We consider the exact S-matrix governing the planar spectral problem for strings on AdS5× S 5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel “boost” symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu(2|2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincar´e supersymmetry algebra, where the deformation parameter is related to the ’t Hooft coupling. We determine the twoparticle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical rmatrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincar´e symmetry, by contraction of the quantum affine algebra Uq(slc2) in Drinfeld’s second realisation.