发表机构
Anqing Normal University; INFN; Scuola Superiore Meridionale; Loyola Marymount University（安庆师范大学; 意大利国家核物理研究所; 南方高等学院; 洛约拉马利蒙特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从前几何规范理论中识别出五个基本构建块，经自发对称破缺统一生成引力的动力学（爱因斯坦-希尔伯特作用量）与拓扑扇区，并揭示跷跷板机制联系普朗克质量与宇宙学常数。
AI 中文摘要
我们识别了四维前几何引力理论的基本构建块的完整集合。基于在未破缺相中一般协变性的刚性约束下与类希格斯场耦合的$SO(1,4)$或$SO(2,3)$规范理论，这些构建块——$\mathcal{L}_\text{MM}$、$\mathcal{L}_\text{W}$、$\mathcal{L}_{J}$、$\mathcal{L}_\theta$和$\mathcal{L}_\vartheta$——构成了独立场单项式的最小生成集，任何前几何作用量（包括其任意泛函）都可以由此构造。虽然最一般的前几何理论可以超越线性组合，但这五个不可约不变量作为所有可能的前几何动力学的“原子”组分。在自发对称破缺后，它们共同生成一个涌现的引力理论，包括爱因斯坦-希尔伯特作用量、宇宙学常数项以及所有四维拓扑不变量：高斯-博内、庞特里亚金、霍尔斯特和聂-严项。引力的动力学与拓扑扇区从共同的前几何源统一，是这项工作的核心结果。我们还揭示了一个跷跷板机制，将普朗克质量和宇宙学常数联系起来，以及拓扑扇区耦合常数的几个新关系，包括巴贝罗-伊米尔齐参数。这一框架建立了前几何基础，所有引力方面都可以从中动态涌现，为量子引力、暗能量现象学和引力理论中拓扑相的研究提供了统一的起点。
英文摘要
We identify the complete set of fundamental building blocks for a 4D pre-geometric theory of gravity. Based on a gauge theory of $SO(1,4)$ or $SO(2,3)$ coupled to a Higgs-like field under the rigid constraint of general covariance in the unbroken phase, these building blocks - $\mathcal{L}_\text{MM}$, $\mathcal{L}_\text{W}$, $\mathcal{L}_{J}$, $\mathcal{L}_θ$ and $\mathcal{L}_\vartheta$ - constitute the minimal generating set of independent field monomials from which any pre-geometric action, including arbitrary functionals thereof, can be constructed. While the most general pre-geometric theory can extend beyond linear combinations, these five irreducible invariants serve as the 'atomic' constituents of all possible pre-geometric dynamics. Upon spontaneous symmetry breaking, they collectively generate an emergent gravitational theory consisting of the Einstein-Hilbert action, the cosmological constant term and all 4D topological invariants: the Gauss-Bonnet, Pontryagin, Holst and Nieh-Yan terms. The unification of gravity's dynamical and topological sectors from a common pre-geometric source represents the central result of this work. We also uncover a see-saw mechanism linking the Planck mass and the cosmological constant, as well as several novel relations for the coupling constants of the topological sector, inclusive of the Barbero-Immirzi parameter. This framework establishes the pre-geometric foundations from which all aspects of gravitation can dynamically emerge, providing a unified starting point for quantum gravity, dark energy phenomenology and the study of topological phases in gravitational theories.
CommentsVersion accepted in PRD
