标题： 在与引力耦合的$O(N)$标量模型中的固有时功能性重整化 显示英文标题

标题： Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity

摘要： 我们关注由适当时间调节器表征的函数Wilsonian重正化群框架的使用，并测试其在寻找与引力耦合的O(N)不变标量场多重态在d=4和d=3维中的标度解和临界性质中的应用。我们采用相同的背景-涨落分解和规范固定过程，这一方法之前在基于有效平均动作框架和有效动作类似截断的研究中已经采用过。我们的主要目标是比较标度解和一些相关临界指数的结果。在这项在不同框架中进行的分析中，之前揭示的大部分图景在定性和定量层面上都得到了确认。然而，在有限N和其大值极限下，也存在一些差异，这还取决于两种框架中称为“改进”的方案。 显示英文摘要

摘要： We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an O(N)-invariant scalar field multiplet coupled to gravity in d=4 and d=3 dimensions. We employ the same background-fluctuation splitting and gauge fixing procedure, already adopted in a previous study based, instead, on the effective average action framework and a similar truncation of the effective action. Our main goal is to compare the results for the scaling solutions and some of the associated critical exponents. In this analysis, performed in a different framework, most of the picture previously uncovered is confirmed both at qualitative and quantitative level. There are, neverthelss, few differences both at finite N and in its large value limit, depending also on the schemes which in both frameworks are called 'improved'