论文标题
保形不变性和重新归一化组
Conformal invariance and Renormalization Group
论文作者
论文摘要
共形场理论（CFT）是一种非常强大的工具，用于在二阶相变或量子关键点上明确计算统计力学系统的关键指数和统计力学系统的相关函数。在适当的平均和重新恢复操作下，共形不变性将是从临界值中从微观模型获得的固定点理论的特征：威尔逊重新归一化组（RG）的作用。不幸的是，一般而言，关键的微观模型与它们的形式不变的缩放极限之间存在明确的联系。尽管如此，过去几十年来，从数学和物理学方面进行了几种新工具，并且它们的应用范围一直在不断而显着增加：我在这里引用了几种新工具，例如，我引用了分离的全态性，sle，sle，sle，sle，sle，lattice病房在建设性RG中使用lattice wart and specorial rg，Gustormal RG，Gustormal bootstrap and Mestall bootstrap and the Comptrap and the Mestall bootstrap and s in 3d cft。为了在这些问题上取得进一步的进展，组织了为期一天的研讨会“统计力学中的新兴CFT”：目的是将概率主义者，数学物理学家和理论物理学家汇总在一起，以互补的工具和连续性的水平，以创建新的方法，从而在关键的统计机制系统的各个方面与批判统计机制系统的各个方面联系在一起。本文基于研讨会上的介绍性谈话：在会议中讨论的主要主题摘要之后，我通过回顾了有关晶状体几何形成中有限范围的关键2D IS与有限范围的关键2D相互作用的关键2D规模限制的最新结果来说明问题的方法。
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a quantum critical point. Conformal invariance is expected to be a feature of the fixed point theory obtained from a microscopic model at criticality, under appropriate averaging and rescaling operations: the action of the Wilsonian Renormalization Group (RG). Unfortunately, an explicit connection between critical microscopic models and their conformally invariant scaling limit is still lacking in general. Nevertheless, the last decades witnessed significant progress on this topic, both from the mathematical and physics sides, where several new tools have been introduced and their ranges of applications have constantly and significantly increased: I refer here, e.g., to discrete holomorphicity, SLE, the use of lattice Ward Identities in constructive RG, the conformal bootstrap program and its recent applications to 3D CFT. In an effort to make further progress on these problems, the one-day workshop "Emergent CFTs in statistical mechanics" was organized: the goal was to bring together probabilists, mathematical physicists and theoretical physicists, working on various aspects of critical statistical mechanics systems with complementary tools, both at the discrete and the continuum level, in the hope of creating new connections between the different approaches. This paper is based on an introductory talk given at the workshop: after a summary of the main topics discussed in the meeting, I illustrate the approach to the problem based on constructive RG methods, by reviewing recent results on the existence and the explicit characterization of the scaling limit of critical 2D Ising models with finite range interactions in cylindrical geometry.
