Massless Flows I:. the Sine-Gordon and O(n) Models
Massless Flows I:. the Sine-Gordon and O(n) Models
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无质量流 I：。
DOI：
10.1142/s0217751x93002265
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发表时间：
1993
影响因子：
1.6
通讯作者：
A. Zamolodchikov
中科院分区：
文献类型：
--
作者：
P. Fendley;H. Saleur;A. Zamolodchikov
共形场论的连续极小模型之间的无质量流动与余弦势系数为虚数时的sine-Gordon模型内的流动有关。这种流动的研究，部分数值，从三个不同的观点。首先，我们计算出接近Kosterlitz无边界点的展开，并获得漫游行为，其中中心电荷在c = 1的UV和IR值之间上下移动。接下来，我们解析地继续质量流的Casimir能量（即具有真实的余弦项）。最后，我们考虑由O（n）模型提供的晶格正则化，其中有质量和无质量流对应于高温和低温相。详细讨论的情况下，n = 0，然后给出使用基本的N = 2的超对称性，这是自发破缺的低温阶段。"指数" trF（− 1）F由Painleve III微分方程得出，并且在这个阶段有简单的极点。这些极点被解释为从能级交叉（聚合物的一维相变）发生。作为应用，得到了圆柱上聚合物图的连通常数的新的精确结果。这些结果和观点在下面的论文中被用来讨论适当的精确S矩阵和由此产生的Casimir能量。
The massless flow between successive minimal models of conformal field theory is related to a flow within the sine-Gordon model when the coefficient of the cosine potential is imaginary. This flow is studied, partly numerically, from three different points of view. First we work out the expansion close to the Kosterlitz-Thouless point, and obtain roaming behavior, with the central charge going up and down in between the UV and IR values of c=1. Next we analytically continue the Casimir energy of the massive flow (i.e. with real cosine term). Finally we consider the lattice regularization provided by the O(n) model in which massive and massless flows correspond to high- and low-temperature phases. A detailed discussion of the case n=0 is then given using the underlying N=2 supersymmetry, which is spontaneously broken in the low-temperature phase. The “index” trF(−1)F follows from the Painleve III differential equation, and is shown to have simple poles in this phase. These poles are interpreted as occurring from level crossing (one-dimensional phase transitions for polymers). As an application, new exact results for the connectivity constants of polymer graphs on cylinders are obtained. These results and points of view are used in the following paper to discuss the appropriate exact S matrices and the resulting Casimir energies.