Geometry of massless scattering in integrable superstring

DOI10.1007/JHEP06(2019)116zbMATH Open1416.83120arXiv1903.10759OpenAlexW2964242552MaRDI QIDQ2314964

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Publication date: 30 July 2019

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Abstract: We consider the action of the $q$-deformed Poincar'e superalgebra on the massless non-relativistic R-matrix in ordinary (undeformed) integrable $Ad{S}_{2}imes{S}^{2}imes{T}^6$ 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) $Ad{S}_{n}imes{S}^{n}imes{T}^{10-2n}$, $n=2,3$. 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.

Full work available at URL: https://arxiv.org/abs/1903.10759

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