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arXiv · 0912.0209

On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra

Gleb Arutyunov·Marius de Leeuw·Alessandro Torrielli
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Abstract

The centrally extended su(2|2) superalgebra is an asymptotic symmetry of the light-cone string sigma model on AdS5 x S5. We consider an evaluation representation of the conventional Yangian built over a particular 16-dimensional long representation of the centrally extended su(2|2). Interestingly, we find that S-matrices compatible with this evaluation representation do not exist. On the other hand, by requiring centrally extended su(2|2) 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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Gleb Arutyunov, Marius de Leeuw, Alessandro Torrielli. 2009-12-01. On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra. https://doi.org/10.1007/jhep06(2010)033

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