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arXiv 1010.0858hep-thcond-mat.stat-mechmath-phmath.MP
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共形场论中的费米子基与激发态的热力学Bethe分析

Fermionic Basis in Conformal Field Theory and Thermodynamic Bethe Ansatz for Excited States

Hermann Boos

发表信息：
SIGMA 7:007,2011
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摘要：

我们将[Comm.Math.Phys.299（2010），825-866，arXiv：0911.3731]的结果（隐藏的格拉斯曼结构IV）推广到六顶点模型的传输矩阵的激发态在所谓的松原方向上作用的情况。我们建立了一个等价的尺度限制的六顶点模型的配分函数的圆柱上插入准局部算子和特殊的边界条件，对应于粒子-空穴激发，一方面，和某些三点关联函数的共形场论（CFT）的另一方面。在隐格拉斯曼结构IV，费米基础上开发的以前的文件和共形限制用于描述的准本地运营商。在论文IV中，我们声称，在共形极限中，费米子创造算子产生的基等价于A. Zamolodchikov（1987）.在这里，我们认为，为了完全确定上述费米子基和CFT中的后代基之间的转换，我们需要涉及激发。在晶格模型的一侧，我们使用激发态TBA方法。我们详细考虑了第8级的后代的情况。

英文摘要：

We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866, arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction. We establish an equivalence between a scaling limit of the partition function of the six-vertex model on a cylinder with quasi-local operators inserted and special boundary conditions, corresponding to particle-hole excitations, on the one hand, and certain three-point correlation functions of conformal field theory (CFT) on the other hand. As in hidden Grassmann structure IV, the fermionic basis developed in previous papers and its conformal limit are used for a description of the quasi-local operators. In paper IV we claimed that in the conformal limit the fermionic creation operators generate a basis equivalent to the basis of the descendant states in the conformal field theory modulo integrals of motion suggested by A. Zamolodchikov (1987). Here we argue that, in order to completely determine the transformation between the above fermionic basis and the basis of descendants in the CFT, we need to involve excitations. On the side of the lattice model we use the excited-state TBA approach. We consider in detail the case of the descendant at level 8.

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