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arXiv 2104.03753gr-qchep-th
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最小变化 $Λ$ 理论的典范结构

Canonical structure of minimal varying $Λ$ theories

Sergei Alexandrov, Simone Speziale, Tom Zlosnik

AI总结:

本文研究了最小变化 $Λ$ 理论的典范结构,发现其为非正则系统,在一般背景下有五个自由度,特定参数条件下减为三个,de Sitter 背景下因共形对称性再减一个,自对偶情形下有两个复自由度。

摘要:

最小变化 $Λ$ 理论由一个作用量定义,该作用量由引力的 Einstein-Cartan-Holst 一阶作用量(将宇宙学常数 $Λ$ 作为独立标量场)构成,并补充了乘以 $1/Λ$ 的 Euler 和 Pontryagin 密度。我们确定了这些理论的典范结构,它们最终代表了非正则系统的一个实例。我们发现,在一般背景和一般参数值下存在五个自由度,而如果参数满足特定条件(包括最常考虑的 Euler 情形),则仅保留三个自由度。在 de Sitter 背景下,典范结构发生变化,由于涌现的共形对称性,谱中减少了一个自由度。我们还分析了自对偶情形,其具有仅依赖于联络自对偶部分的全纯作用量。在此情形下,我们发现了两个(复数)自由度,并进一步讨论了 Kodama 态、对 de Sitter 背景的限制以及现实条件的影响。

英文摘要:

Minimal varying $Λ$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $Λ$ as an independent scalar field, and supplemented by the Euler and Pontryagin densities multiplied by $1/Λ$. We identify the canonical structure of these theories which turn out to represent an example of irregular systems. We find five degrees of freedom on generic backgrounds and for generic values of parameters, whereas if the parameters satisfy a certain condition (which includes the most commonly considered Euler case) only three degrees of freedom remain. On de Sitter-like backgrounds the canonical structure changes, and due to an emergent conformal symmetry one degree of freedom drops from the spectrum. We also analyze the self-dual case with an holomorphic action depending only on the self-dual part of the connection. In this case we find two (complex) degrees of freedom, and further discuss the Kodama state, the restriction to de Sitter background and the effect of reality conditions.

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。

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