Geometry of massless scattering in integrable superstring

Abstract

Abstract We consider the action of the q-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable AdS 2 × S 2 × T 6 type IIB superstring theory. The boost generator acts non-trivially on the R-matrix, confirming the existence of a non-relativistic rapidity γ with respect to which the R-matrix must be of difference form. We conjecture that from a massless AdS/CFT integrable relativistic R-matrix one can obtain the parental massless non-relativistic R-matrix simply by replacing the relativistic rapidity with γ. We check our conjecture in ordinary (undeformed) AdS n × S n × T 10−2n , n = 2,3. In the case n = 3, we check that the matrix part and the dressing factor — up to numerical accuracy for real momenta — obey our prescription. In the n = 2 case, we check the matrix part and propose the non-relativistic dressing factor. We then start a programme of classifying R-matrices in terms of connections on fibre bundles. The conditions obtained for the connection are tested on a set of known integrable R-matrices.