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The Tetrahedral Zamolodchikov Algebra and the \({AdS_5\times S^5}\) S-matrix

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Abstract

The S-matrix of the \({AdS_5\times S^5}\) string theory is a tensor product of two centrally extended su\({(2|2)\ltimes \mathbb{R}^2}\) S-matrices, each of which is related to the R-matrix of the Hubbard model. The R-matrix of the Hubbard model was first found by Shastry, who ingeniously exploited the fact that, for zero coupling, the Hubbard model can be decomposed into two XX models. In this article, we review and clarify this construction from the AdS/CFT perspective and investigate the implications this has for the \({AdS_5\times S^5}\) S-matrix.

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Author notes

  1. Vladimir Mitev

    Present address: PRISMA Cluster of Excellence, Institut für Physik, WA THEP, Johannes Gutenberg-Universität Mainz, Staudingerweg 7, 55128, Mainz, Germany

  2. Zengo Tsuboi

    Present address: Laboratoire de Physique Théorique (LPT ENS), Département de physique de l’ENS, École normale supérieure, PSL Research University, Sorbonne Universités, UPMC Univ. Paris 06, CNRS, 75005, Paris, France

Authors and Affiliations

  1. Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin IRIS Haus, Zum Großen Windkanal 6, 12489, Berlin, Germany

    Vladimir Mitev, Matthias Staudacher & Zengo Tsuboi

  2. Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476, Potsdam, Germany

    Matthias Staudacher

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  1. Vladimir Mitev
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  2. Matthias Staudacher
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  3. Zengo Tsuboi
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Correspondence to Vladimir Mitev.

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Communicated by H.-T. Yau

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Mitev, V., Staudacher, M. & Tsuboi, Z. The Tetrahedral Zamolodchikov Algebra and the \({AdS_5\times S^5}\) S-matrix. Commun. Math. Phys. 354, 1–30 (2017). https://doi.org/10.1007/s00220-017-2905-y

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