论文标题
RG固定点上的可集成Sigma模型：定量为仿射高丁模型
Integrable sigma models at RG fixed points: quantisation as affine Gaudin models
论文作者
论文摘要
本文的目的是通过通过其保形限制来实现这些理论，以使用仿射高丁模型的形式来实现量化可集成的非线性Sigma模型的第一步。我们主要集中在Klimčík模型的示例上，这是在Lie Group $ G $上的主要手性模型的两参数变形。我们表明，该理论的紫外线固定点通过两个脱钩的仿射高丁模型经典描述，编码了其左和右移动的自由度，并对这些模型的手性和整合结构进行了详细的分析。然后在Feigin和Frenkel的框架内探索它们的定量。我们使用定量仿射高丁模型的形式主义研究了量子本地运动积分，并显示了前两个积分与文献中已知结果的一致性，其中$ g = {\ rm su}（2）$。有证据表明存在满足该模型的扬键代数的单型矩阵，从而为非本地运动积分的定量铺平了道路。我们以各种视角结论，包括该程序对较大一类可集成的Sigma模型的概括以及ODE/IQFT对其量子频谱描述的相应的应用。
The goal of this paper is to make first steps towards the quantisation of integrable non-linear sigma models using the formalism of affine Gaudin models, by approaching these theories through their conformal limits. We focus mostly on the example of the Klimčík model, which is a two-parameter deformation of the Principal Chiral Model on a Lie group $G$. We show that the UV fixed point of this theory is described classically by two decoupled chiral affine Gaudin models, encoding its left- and right-moving degrees of freedom, and give a detailed analysis of the chiral and integrable structures of these models. Their quantisation is then explored within the framework of Feigin and Frenkel. We study the quantum local integrals of motion using the formalism of quantised affine Gaudin models and show agreement of the first two integrals with known results in the literature for $G={\rm SU}(2)$. Evidence is given for the existence of a monodromy matrix satisfying the Yang-Baxter algebra for this model, thus paving the way for the quantisation of the non-local integrals of motion. We conclude with various perspectives, including on generalisations of this program to a larger class of integrable sigma models and applications of the ODE/IQFT correspondence to the description of their quantum spectrum.
