标题： 规范理论梯度流精确重整化群的基础 显示英文标题

标题： A basis of the gradient flow exact renormalization group for gauge theory

摘要： 梯度流精确重正化群（GFERG）是精确重正化群（ERG）的一种变体，用于规范理论，旨在尽可能明显地保持规范不变性。 它通过利用杨-米尔斯梯度流或扩散来进行块自旋过程来实现这一目标。 在本文中，我们通过Reuter方程来表述GFERG，其中块自旋是通过高斯积分完成的。 这种表述提供了一种对GFERG各种尚未解决的要点的简单理解。 首先，在GFERG方程中存在一种唯一的泛函导数顺序，可以消除接触项的歧义。 其次，如果未引入规范固定，GFERG的微扰理论会遭受非传统的紫外（UV）发散。 这解释了我们在GFERG微扰解中遇到的一些UV发散的起源。 第三，使用GFERG中的威尔逊作用量计算的修正关联函数与使用裸作用量计算的扩散或流动场的关联函数一致。 这表明存在一个威尔逊作用量，可以精确再现由梯度流形式主义计算的物理量（除去接触项）。 我们获得了梯度流的明确重正化群解释。 本文给出的表述为在GFERG中进行进一步的微扰/非微扰计算提供了基础，同时最大程度地保持规范不变性。 显示英文摘要

摘要： The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed to preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the Yang--Mills gradient flow or diffusion for the block-spin process. In this paper, we formulate GFERG by the Reuter equation in which the block spinning is done by Gaussian integration. This formulation provides a simple understanding of various points of GFERG, unresolved thus far. First, there exists a unique ordering of functional derivatives in the GFERG equation that remove ambiguity of contact terms. Second, perturbation theory of GFERG suffers from unconventional ultraviolet (UV) divergences if no gauge fixing is introduced. This explains the origin of some UV divergences we have encountered in perturbative solutions to GFERG. Third, the modified correlation functions calculated with the Wilson action in GFERG coincide with the correlation functions of diffused or flowed fields calculated with the bare action. This shows the existence of a Wilson action that reproduces precisely the physical quantities computed by the gradient flow formalism (up to contact terms). We obtain a definite ERG interpretation of the gradient flow. The formulation given in this paper provides a basis for further perturbative/non-perturbative computations in GFERG, preserving gauge invariance maximally.