arXiv 2202.087682022-02hep-thgr-qc

具有负宇宙学常数的卡洛引力理论的渐近对称性

Asymptotic symmetries in Carrollian theories of gravity with a negative cosmological constant

Alfredo Pérez

备注：: 22 pages, no figures. The introduction was expanded. An appendix and two footnotes have been added. Some minor corrections were also implemented. Matches published version in JHEP
DOI：: 10.1007/JHEP09(2022)044

摘要：

在3+1维时空中，分析了具有负宇宙学常数$Λ$的电磁卡罗引力理论的渐近对称性.在磁理论中，渐近对称代数由三维共形Carroll代数给出，它是无限维的，同构于BMS $_{4}$代数。这些结果与全息理论的预期完全一致，为研究“卡罗利全息”提供了一个新的框架。“相反，在电学理论的情况下，负$Λ$的存在被证明与一组一致的渐近条件不相容，这可以追溯到不存在可感知的基态构型。如果考虑从欧几里德广义相对论的电收缩得到的卡罗理论，这一点可以得到改进。在这种情况下，渐近条件可以用$so\left(1,4\right)$给出的渐近对称代数来构造。然而，它表明，该理论的球对称解的空间是退化的。

英文摘要：

Asymptotic symmetries of electric and magnetic Carrollian gravitational theories with a negative cosmological constant $Λ$ are analyzed in 3+1 space-time dimensions. In the magnetic theory, the asymptotic symmetry algebra is given by the conformal Carroll algebra in three dimensions, which is infinite-dimensional and isomorphic to the BMS$_{4}$ algebra. These results are in full agreement with holographic expectations, providing a new framework for the study of "Carrollian holography." On the contrary, in the case of the electric theory, the presence of a negative $Λ$ turns out to be incompatible with a consistent set of asymptotic conditions, that can be traced back to the absence of a sensible ground state configuration. This can be improved if the Carrollian theory obtained from an electric contraction of Euclidean General Relativity is considered. In this case, asymptotic conditions can be constructed with an asymptotic symmetry algebra given by $so\left(1,4\right)$. However, it is shown that the space of spherically symmetric solutions of this theory is degenerate.

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