Abstract
The centrally extended \( \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) \) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS5 × S5. We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long representation of the centrally extended \( \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) \). Interestingly, we find that S-matrices compatible with this evaluation representation do not exist. On the other hand, by requiring centrally extended \( \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) \) invariance and explicitly solving the Yang-Baxter equation, we find a scattering matrix for long-short representations of the Lie superalgebra. We notice that this S-matrix is invariant under a different representation of non-evaluation type, induced from the tensor product of short representations. Our findings concern the conventional Yangian only, and are not applied to possible algebraic extensions of the latter.
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ArXiv ePrint: 0912.0209
Correspondent fellow at Steklov Mathematical Institute, Moscow, Russia (Gleb Arutyunov)
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Arutyunov, G., de Leeuw, M. & Torrielli, A. On Yangian and long representations of the centrally extended \( \mathfrak{s}\mathfrak{u}\left( {\left. 2 \right|2} \right) \) superalgebra. J. High Energ. Phys. 2010, 33 (2010). https://doi.org/10.1007/JHEP06(2010)033
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DOI: https://doi.org/10.1007/JHEP06(2010)033