论文标题
通过收缩和减少的ADS/CFT可集成性的经典谎言双gebras
Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
论文作者
论文摘要
一维Hubbard模型以及在ADS字符串中遇到的分支散射问题的整合性可以用特殊的量子代数表示。在本文中，我们基于既定的简单谎言superalgebra d（2,1; epsilon）的既定结果来得出这些代数可集成结构的经典限制，以及在3D ADS空间上形成超对称异构的标准SL（2）。该结构中的两个主要步骤包括3DPoincaréSuperalgebra的收缩，并降低了U（2 | 2）Superalgebra的变形。我们将这些步骤应用于可集成的结构，并以合理的理性和三角学类型的经典R-Matrices获得所需的谎言。我们用广告和平面空间的壳场的表示形式来说明我们的发现。
Integrability of the one-dimensional Hubbard model and of the factorised scattering problem encountered on the worldsheet of AdS strings can be expressed in terms of a peculiar quantum algebra. In this article, we derive the classical limit of these algebraic integrable structures based on established results for the exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) which form supersymmetric isometries on 3D AdS space. The two major steps in this construction consist in the contraction to a 3D Poincaré superalgebra and a certain reduction to a deformation of the u(2|2) superalgebra. We apply these steps to the integrable structure and obtain the desired Lie bialgebras with suitable classical r-matrices of rational and trigonometric kind. We illustrate our findings in terms of representations for on-shell fields on AdS and flat space.
