来自不变Weyl-可积时空（IWIST）的引力

中文摘要 AI 辅助

在本文中，我们提出了一种在不变Weyl-可积时空（IWIST）中基于几何动机的引力表述，其中背景几何并非先验强加，而是通过Palatini变分原理动态确定。对于非最小耦合到引力作用的标量场，由此产生的相容性条件定义了一种Weyl-可积几何，该几何在度量和几何标量场的局部Weyl变换下保持不变。我们构造了一个在微分同胚和Weyl变换下均不变的作用量，并引入了一种基于散度定理不变扩展的Weyl协变变分程序。相应地，我们得到了度规、Weyl标量和Weyl规范场的场方程。我们进一步在爱因斯坦-黎曼框架中表述该理论，其中有效度规是黎曼的，标量场被重新解释为具有几何起源的物理自由度。最后，我们提出了一种通过引入Weyl规范场与由标量扇区构造的流之间的耦合来显式破缺Weyl对称性的几何机制。所得理论保持微分同胚协变性，同时偏离局部Weyl不变性。破缺理论的爱因斯坦-黎曼表示包含一个额外的广义协变相互作用，使得Weyl不变模型成为更一般引力理论的一个特定极限。

英文摘要

In this paper we propose a geometrically motivated formulation of gravity in an invariant Weyl--Integrable space-time (IWIST), in which the background geometry is not imposed a priori but is dynamically determined through the Palatini variational principle. For a scalar field non-minimally coupled to gravity action, the resulting compatibility condition defines a Weyl--Integrable geometry which is preserved by a local Weyl transformation of the metric and the geo\-me\-tri\-cal scalar field. We construct an action invariant under both diffeomorphisms and Weyl transformations and introduce a Weyl-covariant variational procedure based on an invariant extension of the divergence theorem. The corresponding field equations are obtained for the metric, the Weyl scalar, and the Weyl gauge field. We further formulate the theory in the Einstein--Riemann frame, where the effective metric is Riemannian and the scalar field is re\-inter\-pre\-ted as a phy\-si\-cal degree of freedom of geometric origin. Finally, we propose a geometrical mechanism for the explicit breaking of Weyl symmetry by introducing a coupling between the Weyl gauge field and a current constructed from the scalar sector. The resulting theory remains diffeomorphism covariant while departing from local Weyl invariance. The Einstein--Riemann representation of the broken theory contains an additional generally covariant interaction, making the Weyl-invariant model a particular limit of a more general gravitational theory.

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24 pages, no figures