arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1601.08211hep-th
收藏

张量群场论在$\mathbb{R}^d$上的泛函重整化群分析

Functional Renormalisation Group analysis of Tensorial Group Field Theories on $\mathbb{R}^d$

Joseph Ben Geloun, Riccardo Martini, Daniele Oriti

备注：
43 pages, 9 figures
发表信息：
Phys. Rev. D 94, 024017 (2016)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

秩d张量群场论是定义在群流形$G^{\times d}$上的量子场论，它代表了标准QFT的非定域推广，也是量子引力的候选形式，因为当赋予适当的数据时，它们可以被解释为定义了量子时空基本构建块的场论描述。它们的重整化分析对于建立它们作为量子场论的一致性，以及研究连续时空和几何的出现都是至关重要的。在本文中，我们研究的重整化群流的两个简单的类的TGFTs，定义为组$G=\mathbb{R}$任意秩，没有和规范不变的条件下，通过功能重整化群技术。IR发散的问题是通过定义适当的TGFTs的热力学极限来解决的。我们映射这样的模型的相图，在一个简单的截断，并确定UV和IR的RG流的固定点。令人鼓舞的是，对于我们研究的所有模型，我们发现的证据存在一个相变的冷凝类型。

英文摘要：

Rank-d Tensorial Group Field Theories are quantum field theories defined on a group manifold $G^{\times d}$, which represent a non-local generalization of standard QFT, and a candidate formalism for quantum gravity, since, when endowed with appropriate data, they can be interpreted as defining a field theoretic description of the fundamental building blocks of quantum spacetime. Their renormalisation analysis is crucial both for establishing their consistency as quantum field theories, and for studying the emergence of continuum spacetime and geometry from them. In this paper, we study the renormalisation group flow of two simple classes of TGFTs, defined for the group $G=\mathbb{R}$ for arbitrary rank, both without and with gauge invariance conditions, by means of functional renormalisation group techniques. The issue of IR divergences is tackled by the definition of a proper thermodynamic limit for TGFTs. We map the phase diagram of such models, in a simple truncation, and identify both UV and IR fixed points of the RG flow. Encouragingly, for all the models we study, we find evidence for the existence of a phase transition of condensation type.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑