论文标题
自动对称，字符串可集成结构和变形
Automorphic Symmetries, String integrable structures and Deformations
论文作者
论文摘要
我们探讨了在量子和弦的可集成理论中产生的新结构，以及构造方法以获取它们并提供进一步的分析。具体而言，我们在周期性晶格系统上实现了自动形态对称性，以获得可集成的层次结构，其通勤性和可集成的转换会导致可集成类的生成结构。该处方首先应用于2-DIM和4-DIM设置，在那里我们找到新的$ \ Mathfrak {SL} _ {2} $ sector，$ \ Mathfrak {Su}（2）\ oplus \ oplus \ mathfrak {su}（su}（su}（2）$，具有超管模式，常规模式，通用的Hubbard类型类别和更多。相应的2-和4-DIM $ r $矩阵通过扰动理论解决，可以恢复确切的结果。然后，我们构建了一个提升递归，该递归允许解决该系统，该系统的$ r $ - /$ s $ - matrices具有任意的频谱依赖性，这也是散射运算符在$ ADS $集成性中的明显属性。然后，可以在$ d = 2,3,4 $中实现哈密顿安塞特兹的最后一个，从而在所有维度上都带来新的模型。我们还提供了一种基于耦合差分系统的方法，该系统允许准确地解决$ r $矩阵。重要的是，在二-DIM情况（6VB/8VB）中，可能孤立了一类非差异形式的特殊模型，该模型在$ ads_ {3} $和$ ads_ {2} $字符串背景中提供了一种新结构。我们证明，这些类可以表示为$ ads _ {\ {2,3 \}} $模型的变形。我们还解决了后者，后者满足自由费用的约束，编织单位性，交叉和展示变形的代数结构，该结构与$ ads_ {3} \ times s^{3} \ times s^{3} \ times \ times \ times \ Mathcal \ Mathcal {M}^{M}^{4}^{4} $和$ ads_和$ aD} $ {2} 2} $}^$证明了6VB/8VB变形的嵌入和映射，提供了与Sigma模型候选者有关的讨论。
We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on periodic lattice systems to obtain integrable hierarchies, whose commutativity and integrable transformations induce a generating structure of integrable classes. This prescription is first applied to 2-dim and 4-dim setups, where we find the new $ \mathfrak{sl}_{2} $ sector, $ \mathfrak{su}(2) \oplus \mathfrak{su}(2) $ with superconductive modes, Generalised Hubbard type classes and more. The corresponding 2- and 4-dim $ R $ matrices are resolved through perturbation theory, that allows to recover an exact result. We then construct a boost recursion that allows to address the systems, whose $ R $-/$ S $-matrices exhibit arbitrary spectral dependence, that also is an apparent property of the scattering operators in $ AdS $ integrability. It is then possible to implement the last for Hamiltonian Ansätze in $ D = 2,3,4 $, which leads to new models in all dimensions. We also provide a method based on a coupled differential system that allows to resolve for $ R $ matrices exactly. Important it is possible isolate a special class of models of non-difference form in 2-dim case (6vB/8vB), which provides a new structure consistently arising in $ AdS_{3} $ and $ AdS_{2} $ string backgrounds. We prove that these classes can be represented as deformations of the $ AdS_{\{ 2,3 \}} $ models. We also work out that the latter satisfy free fermion constraint, braiding unitarity, crossing and exhibit deformed algebraic structure that shares certain properties with $ AdS_{3} \times S^{3} \times \mathcal{M}^{4} $ and $ AdS_{2} \times S^{2} \times T^{6} $ models. The embedding and mappings of 6vB/8vB deformations are demonstrated, a discussion on relation to sigma model candidates is provided.
