$q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$

Abstract

We consider the exact S-matrix governing the planar spectral problem for strings on $Ad{S}_5\times S^5$ 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.

35 pages. Added discussion on antipode in the presence of the phase. Published version

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• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Nonlocal Symmetries and Factorized Scattering
• Boost generator in AdS_3 integrable superstrings for general braiding
• A study of integrable form factors in massless relativistic AdS_3
• Geometry of Massless Scattering in Integrable Superstring
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction