The bound state S-matrix for \(AdS_{5}\times S^{5}\) superstring. (English) Zbl 1194.81181
Summary: We determine the S-matrix that describes scattering of arbitrary bound states in the light-cone string theory in \(AdS_{5}\times S^{5}\). The corresponding construction relies on the Yangian symmetry and the superspace formalism for the bound state representations. The basic analytic structure supporting the S-matrix entries turns out to be the hypergeometric function \({}_4F_3\). We show that for particular bound state numbers it reproduces all the scattering matrices previously obtained in the literature. Our findings should be relevant for the TBA and Lüscher approaches to the finite-size spectral problem. They also shed some light on the construction of the universal R-matrix for the centrally-extended \({\mathfrak psu}(2|2)\) superalgebra.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 17A70 | Superalgebras |
Keywords:
light-cone string theory; Yangian symmetry; superspace formalism; Lüscher spectral problem approachesReferences:
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