Geometry of Massless Scattering in Integrable Superstring

Abstract

We consider the action of the $q$-deformed Poincaré superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable $Ad{S}_2\times S^2\times T^6$ type IIB superstring theory. The boost generator acts non-trivially on the R-matrix, confirming the existence of a non-relativistic rapidity $\gamma$ 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 $\gamma$. We check our conjecture in ordinary (undeformed) $Ad{S}_n\times S^n\times T^{10-2n}$, $n=2,3$. 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.

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Cited by in corpus (2)

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• On the singularities of the R-R AdS_3 x S^3 x T^4 S matrix