On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
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.
Keywords
Cite
@article{arxiv.0912.0209,
title = {On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra},
author = {Gleb Arutyunov and Marius de Leeuw and Alessandro Torrielli},
journal= {arXiv preprint arXiv:0912.0209},
year = {2014}
}
Comments
Version accepted for publication in JHEP