Abstract

We develop a technique based on the boost automorphism for finding new lattice integrable models with various dimensions of local Hilbert spaces. We initiate the method by implementing it in two-dimensional models and resolve a classification problem, which not only confirms the known vertex model solution space but also extends to the new \(\mathfrak{sl}_2\) deformed sector. A generalization of the approach to integrable string backgrounds is provided and allows finding new integrable deformations and associated \(R\)-matrices. The new integrable solutions appear to be of a nondifference or pseudo-difference form admitting \(AdS_2\) and \(AdS_3\) \(S\)-matrices as special cases (embeddings), which also includes a map of the double-deformed sigma model \(R\)-matrix. The corresponding braiding and conjugation operators of the novel models are derived. We also demonstrate implications of the obtained free-fermion analogue for \(AdS\) deformations.

中文翻译：

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弦论中自守对称的新可积性

摘要

我们开发了一种基于增强自同构的技术，用于寻找具有不同维度的局部希尔伯特空间的新格可积模型。我们通过在二维模型中实现该方法来启动该方法并解决分类问题，这不仅确认了已知的顶点模型解空间，而且还扩展到了新的\(\mathfrak{sl}_2\)变形扇区。提供了可积弦背景方法的概括，并允许找到新的可积变形和关联的\(R\)矩阵。新的可积解似乎是非差分或伪差分形式，承认\(AdS_2\)和\(AdS_3\) \(S\)矩阵作为特殊情况（嵌入），其中还包括双矩阵的映射变形西格玛模型\(R\) -矩阵。推导了新模型相应的编织算子和共轭算子。我们还证明了所获得的自由费米子类似物对AdS变形的影响。