标题： 从Gaudin自旋链中的σ模型 显示英文标题

标题： Sigma models from Gaudin spin chains

摘要： 我们解决了1D sigma模型的经典和量子问题，其目标空间是旗流形$\mathrm{U}(3)\over \mathrm{U}(1)^3$，并配备了最一般的不变度量。 特别是，我们明确地用椭圆函数描述了所有测地线，并证明拉普拉斯-贝尔特拉米算子的谱可以通过求解多项式（Bethe）方程来获得。 我们使用的主要技术工具是sigma模型与Gaudin模型之间的映射，该映射也被证明在$\mathrm{U}(n)$的情况下成立。 显示英文摘要

摘要： We solve the classical and quantum problems for the 1D sigma model with target space the flag manifold $\mathrm{U}(3)\over \mathrm{U}(1)^3$, equipped with the most general invariant metric. In particular, we explicitly describe all geodesics in terms of elliptic functions and demonstrate that the spectrum of the Laplace-Beltrami operator may be found by solving polynomial (Bethe) equations. The main technical tool that we use is a mapping between the sigma model and a Gaudin model, which is also shown to hold in the $\mathrm{U}(n)$ case.