论文标题
SuperString Sigma-Models中的谎言代数扩展和集成性
Lie Algebra Expansion and Integrability in Superstring Sigma-Models
论文作者
论文摘要
Lie代数扩展是一种从给定的技术生成新的谎言代数的技术。在本文中，我们将Lie代数扩展的方法应用于具有$ \ Mathbb {Z} _4 $ coset目标空间的SuperString $σ$ -MODEL。通过将LIE代数扩展应用于等轴测代数，我们获得了不同的$σ$ - 模型，其中动态场的数量可能会更改。我们以某种已知的弦乐制度（ADS $ _5 \ times $ s $^5 $）的系统方式进行复制和扩展。我们定义了代数截断的标准，以便新的$σ$ - 模型的扩展动作的运动方程等于通过扩展初始模型的LAX连接获得的LAX连接的消失曲率条件。
Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring $σ$-models with a $\mathbb{Z}_4$ coset target space. By applying the Lie algebra expansion to the isometry algebra, we obtain different $σ$-models, where the number of dynamical fields can change. We reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS$_5 \times$S$^5$). We define a criterion for the algebra truncation such that the equations of motion of the expanded action of the new $σ$-model are equivalent to the vanishing curvature condition of the Lax connection obtained by expanding the Lax connection of the initial model.
