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arXiv · 1706.10265

$q$-Poincaré supersymmetry in $AdS_5/CFT_4$

Riccardo Borsato·Alessandro Torrielli
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Abstract

We consider the exact S-matrix governing the planar spectral problem for strings on $AdS_5\times S^5$ and $\mathcal N=4$ super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended $\mathfrak{psu}(2|2)$ symmetry, and to conclude that the S-matrix is invariant under a $q$-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra $U_q(\widehat{\mathfrak{sl}_2})$ in Drinfeld's second realisation.

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Riccardo Borsato, Alessandro Torrielli. 2018-02-20. $q$-Poincaré supersymmetry in $AdS_5/CFT_4$. https://doi.org/10.1016/j.nuclphysb.2018.01.017

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