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arXiv 1711.02446hep-th
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$AdS_3/CFT_2$ $R$ -矩阵的$q$ -Poincaré不变性

$q$-Poincaré invariance of the $AdS_3/CFT_2$ $R$-matrix

Riccardo Borsato, Joakim Strömwall, Alessandro Torrielli

备注：
26 pages. Minor improvements and references added. Published version
发表信息：
Phys. Rev. D 97, 066001 (2018)
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摘要：

我们考虑的$R$ -矩阵的$AdS_3/CFT_2$，这是用于描述的光锥规范固定的背景$AdS_3 \times S^3 \times T^4$和$AdS_3 \times S^3 \times S^3 \times S^1$与纯Ramond-Ramond通量的世界面激发的散射的积木。我们证明了$R$在“变形的boost”对称性下是不变的，为此我们写出了一个明确的精确余积，即它对2粒子态的作用。当我们包含boost时，$R$ -矩阵的对称性接近于一个$q$ -Poincaré超代数。我们的研究结果表明，最近发现的增强不变性在$AdS_5/CFT_4$可能是一个共同的特点，$AdS/CFT$系统，可处理的确切技术的可积性。随着对一个普遍的制定的基础Hopf代数的目的，我们还提出了一个普遍形式的$AdS_3/CFT_2$经典$r$矩阵。

英文摘要：

We consider the exact $R$-matrix of $AdS_3/CFT_2$, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^3 \times S^3 \times S^1$ with pure Ramond-Ramond fluxes. We show that $R$ is invariant under a "deformed boost" symmetry, for which we write an explicit exact coproduct, i.e. its action on 2-particle states. When we include the boost, the symmetries of the $R$-matrix close into a $q$-Poincaré superalgebra. Our findings suggest that the recently discovered boost invariance in $AdS_5/CFT_4$ may be a common feature of $AdS/CFT$ systems that are treatable with the exact techniques of integrability. With the aim of going towards a universal formulation of the underlying Hopf algebra, we also propose a universal form of the $AdS_3/CFT_2$ classical $r$-matrix.

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