发表机构
Department of Physics, Faculty of Science, Ferdowsi University of Mashhad; School of Physics, Institute for Research in Fundamental Sciences (IPM)（马什哈德费尔多西大学理学院物理系; 基础科学研究院物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Carrollian引力的三位一体框架，证明磁性Carrollian引力可通过联络自由度等价转化为挠率、非度规性及多种非引力理论，建立几何与规范理论的对应字典。
AI 中文摘要
在本文中，我们将引力的几何三位一体范式扩展到Carrollian几何，以构建磁性Carrollian引力的动力学等价理论的综合框架。利用退化度规上仿射联络固有的歧义性和自由度，我们系统地放宽了刚性磁性扇区的度规相容性和零挠率约束。通过对这些修正联络施加全局平坦性，我们证明了磁性Carrollian宇宙的曲率可以动力学地转化为挠率和非度规性的孤立动能密度。与将引力映射到替代引力框架的Lorentzian三位一体不同，Carrollian等价关系还可以将时空几何映射到非引力理论。具体而言，我们证明了内禀挠率恢复出Electric Carrollian引力，作为磁性Carroll引力的Teleparallel等价；纯空间挠率再现出与标量电荷Fracton规范理论的磁性哈密顿量结构相似的动能项；而时间挠率扇区分别独立映射到$U(1)$麦克斯韦电场和Carroll-Weyl共形膨胀子理论。最后，通过构造具有最小非度规性的对称Teleparallel Carroll联络，我们表明在利用联络中现有自由度的条件下，磁性Carrollian拉格朗日量在动力学上等价于一个超局域的、各向同性的Electric Carrollian引力。这些结果建立了一个几何字典，将Carrollian引力动力学翻译为张量规范理论、电磁学和膨胀子理论的语言。
英文摘要
In this paper, we extend the paradigm of the Geometrical Trinity of Gravity to the Carrollian geometry to construct a comprehensive framework of dynamically equivalent theories for Magnetic Carrollian gravity. Utilizing the inherent ambiguities and freedoms of affine connections on degenerate metrics, we systematically relax the metric-compatibility and zero-torsion constraints of the rigid magnetic sector. By imposing global flatness on these modified connections, we prove that the curvature of a Magnetic Carrollian universe can be dynamically traded for isolated kinetic energy densities of torsion and non-metricity. Unlike the Lorentzian Trinity which maps gravity to alternative gravitational frameworks, the Carrollian equivalences can also map spacetime geometry to non-gravitational theories. Specifically, we demonstrate that intrinsic torsion recovers Electric Carrollian gravity as the Teleparallel equivalent of Magnetic Carroll gravity; purely spatial torsion reproduces kinetic terms stracturally similar to the magnetic Hamiltonian of scalar-charge Fracton gauge theory; and temporal torsion sectors map independently to $U(1)$ Maxwell electric fields and Carroll-Weyl conformal dilaton theories. Finally, by formulating a Symmetric Teleparallel Carroll connection with minimal non-metricity, we show that the Magnetic Carrollian Lagrangian is dynamically equivalent to an ultralocal, isotropic Electric Carrollian gravity upon exploiting the present freedoms in connection. These results establish a geometric dictionary translating Carrollian gravitational dynamics into the language of tensor gauge theories, electromagnetism, and dilaton theory.
Comments48 pages, 2 figures, 3 tables,
