Abstract
We construct a relativistic scattering theory based on a q deformation and large string tension limit of the magnon S-matrix of the string world sheet theory in AdS5 × S 5. The S-matrix falls naturally into a previously studied class associated to affine quantum groups, in this case for a twisted affine loop superalgebra associated to an outer automorphism of (2|2). This infinite algebra includes the celebrated triply extended superalgebra \( \left( {{2}|{2}} \right) \ltimes {\mathbb{R}^{{3}}} \), but only two of the centres, the lightcone components of the 2-momentum, are non-vanishing. The algebra has the interpretation as an extended supersymmetry algebra including a non-trivial R-symmetry. The representation theory of this algebra has some complications in that tensor products are reducible but indecomposable; however, we find that structure meshes perfectly with the bootstrap, or fusion, equations of S-matrix theory. The bootstrap equations can then be used inductively to generate the complete S-matrix. Unlike the magnon theory, the relativistic theory only has a finite set of states and we find that — at least when the deformation parameter q is a root of unity — the spectrum matches precisely the soliton spectrum of the relativistic theory underlying the Pohlmeyer reduction of the string world sheet theory known as the semi-symmetric space sine-Gordon theory.
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Hoare, B., Hollowood, T.J. & Miramontes, J.L. A relativistic relative of the magnon S-matrix. J. High Energ. Phys. 2011, 48 (2011). https://doi.org/10.1007/JHEP11(2011)048
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DOI: https://doi.org/10.1007/JHEP11(2011)048