标题： 渐近 CFT 的可积理论 显示英文标题

标题： Integrable theories that are asymptotically CFT

摘要： 对一系列具有挠率的σ模型进行了分析，这些模型能够动态生成质量，但其紫外固定点是非平凡的共形场论——实际上是SU(2) WZW模型，且处于第$k$级别。 与更熟悉的渐近自由理论的情况形成对比，在渐近自由理论中固定点是平凡的，这里考虑的σ模型可以被称为“渐近共形场论”。 这些理论之前被推测为量子可积；这一点通过假设一个可因子化的S-矩阵来描述它们的红外行为，并随后对该提议进行严格的检验得以确认。 该检验涉及将理论耦合到守恒荷，并计算自由能的一阶微扰展开和直接从S-矩阵通过零温化学势下的热力学Bethe假设得到的结果。 比较这些结果为所提出的S-矩阵提供了令人信服的证据；它还给出了β函数的普适系数，并允许以$1/k$的一级精度评估质量间隙（物理质量与$\Lambda$参数之比）。 显示英文摘要

摘要： A series of sigma models with torsion are analysed which generate their mass dynamically but whose ultra-violet fixed points are non-trivial conformal field theories -- in fact SU(2) WZW models at level $k$. In contrast to the more familiar situation of asymptotically free theories in which the fixed points are trivial, the sigma models considered here may be termed ``asymptotically CFT''. These theories have previously been conjectured to be quantum integrable; this is confirmed by postulating a factorizable S-matrix to describe their infra-red behaviour and then carrying out a stringent test of this proposal. The test involves coupling the theory to a conserved charge and evaluating the response of the free-energy both in perturbation theory to one loop and directly from the S-matrix via the Thermodynamic Bethe Ansatz with a chemical potential at zero temperature. Comparison of these results provides convincing evidence in favour of the proposed S-matrix; it also yields the universal coefficients of the beta-function and allows for an evaluation of the mass gap (the ratio of the physical mass to the $\Lambda$-parameter) to leading order in $1/k$.