标题： 可积理论的渐近CFT 显示英文标题

标题： Integrable theories that are asymptotically CFT

摘要： 一系列具有扭力的sigma模型被分析，这些模型通过动态生成质量，但其紫外固定点是非平凡的共形场理论——实际上是在 level $k$的 SU(2) WZW 模型。 与更熟悉的渐近自由理论中固定点为平凡的情况相反，此处考虑的sigma模型可以称为“渐近CFT”。 这些理论之前已被推测为量子可积；通过假设一个可分解的S矩阵来描述其红外行为，并对这一假设进行严格的测试，从而得到确认。 该测试包括将理论耦合到一个守恒电荷，并在微扰理论中进行一环计算以及通过热力学Bethe假设在零温度下使用化学势直接从S矩阵评估自由能。 比较这些结果提供了有力的证据支持所提出的S矩阵；它还给出了beta函数的通用系数，并允许在 $1/k$的主导阶次下评估质量间隙（物理质量与 $\Lambda$-参数的比值）。 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 $1/k$.