论文标题
2D边界流的RG接口的属性
Properties of RG interfaces for 2D boundary flows
论文作者
论文摘要
我们考虑在二维QFT中边界RG流的RG接口。此类接口是连接紫外线和IR共形边界条件的特定边界条件。我们将它们称为RG操作员。在本文中，我们研究了他们的一般特性，提出了许多猜想。我们猜想RG操作员始终是保形的主要原理，因此该操作员的OPE及其偶联物必须在以一个顺序和领先的无关运算符（当时存在的情况下）时，将流量输入IR固定点时，必须包含扰动的UV操作员。我们通过扰动计算附近固定点之间的流量来支持我们的猜想，这是一种非扰动变异方法，灵感来自J. Cardy提出的大量RG流的变异方法，以及使用边界TCSA获得的数值结果。变分方法具有自己的优点，因为它可以用作绘制边界RG流动空间的整体结构的第一个近似值。我们还讨论了RG运营商在国家和地方运营商的运输中的作用。我们的某些考虑可以推广到二维批量流，阐明了D.
We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J.~Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D.~Gaiotto for bulk $ϕ_{1,3}$ flows.
