标题： 关于$2d$可积模型的空间 显示英文标题

标题： On the space of $2d$ integrable models

摘要： 我们研究无限维李代数，其无限维互相同交换的子代数对应于$2d$可积模型的对称性代数。 这些李代数由具有左（右）移动或者（反）全纯电流的理论中存在的无穷小、非线性和高阶导数对称变换的集合来定义。我们研究了这类拉格朗日理论的一个广泛类别。 我们研究了$2d$自由无质量标量的交换子代数，并找到了正弦-戈登、刘维尔、布尔洛夫-多德和克尔德夫-德弗里斯等已知可积模型的对称性。 在此过程中，我们发现了几个新的交换荷序列，我们推测它们是单个标量的新变形的可积模型的荷。 量子化后，李代数会发生形变，其交换子代数也会随之形变。 显示英文摘要

摘要： We study infinite dimensional Lie algebras, whose infinite dimensional mutually commuting subalgebras correspond with the symmetry algebra of $2d$ integrable models. These Lie algebras are defined by the set of infinitesimal, nonlinear, and higher derivative symmetry transformations present in theories with a left(right)-moving or (anti)-holomorphic current. We study a large class of such Lagrangian theories. We study the commuting subalgebras of the $2d$ free massless scalar, and find the symmetries of the known integrable models such as sine-Gordon, Liouville, Bullough-Dodd, and Korteweg-de Vries. Along the way, we find several new sequences of commuting charges, which we conjecture are charges of integrable models which are new deformations of a single scalar. After quantizing, the Lie algebra is deformed, and so are their commuting subalgebras.