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arXiv 2008.09181hep-thgr-qc
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量子引力的不动点与UV临界曲面的维度

Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface

Yannick Kluth, Daniel Litim

备注：
62 pages, 28 figures. Added more discussions and explanations. Revised several plots. Version accepted for publication with PRD
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AI总结：

本研究利用泛函重整化群研究广义相对论高阶曲率延拓的量子效应，检验量子引力的渐近安全猜想，发现量子诱导的标度维度偏移可产生四维UV临界曲面，提出识别稳定本征向量的等权重条件，为量子引力研究提供新结果。

摘要：

我们利用泛函重整化群研究广义相对论高阶曲率延拓中的量子效应，推导了包含里奇标量、里奇张量和黎曼张量相互作用的一般类别模型的新流方程。我们将该方法应用于检验量子引力的渐近安全猜想，所研究的多项式黎曼张量相互作用形式为$\sim\int \sqrt{g} \\,(R_{μνστ}R^{μνστ})^n$、$\sim\int \sqrt{g} \\, R\cdot(R_{μνστ}R^{μνστ})^n$及其函数形式。通过结合高阶多项式近似、Padé重求和和全数值积分，我们确定了相互作用不动点、普适标度维度、本征值谱的能隙、量子运动方程和德西特解。最值得注意的是，我们发现量子诱导的标度维度偏移可产生四维紫外（UV）临界曲面。维度更高的相互作用仍保持无关性，表现出近高斯标度和弱耦合特征。此外，我们提出了一种新的等权重条件，用于识别展开中所有阶的稳定本征向量。本文还强调了与Einstein-Hilbert近似、$f(R)$近似和$f(R,{\rm Ric}^2)$模型结果的异同，并讨论了这些发现对量子引力和渐近安全猜想的意义。

英文摘要：

We study quantum effects in higher curvature extensions of general relativity using the functional renormalisation group. New flow equations are derived for general classes of models involving Ricci scalar, Ricci tensor, and Riemann tensor interactions. Our method is applied to test the asymptotic safety conjecture for quantum gravity with polynomial Riemann tensor interactions of the form $\sim\int \sqrt{g} \,(R_{μνστ}R^{μνστ})^n$ and $\sim\int \sqrt{g} \, R\cdot(R_{μνστ}R^{μνστ})^n$, and functions thereof. Interacting fixed points, universal scaling dimensions, gaps in eigenvalue spectra, quantum equations of motion, and de Sitter solutions are identified by combining high order polynomial approximations, Padé resummations, and full numerical integration. Most notably, we discover that quantum-induced shifts of scaling dimensions can lead to a four-dimensional ultraviolet critical surface. Increasingly higher-dimensional interactions remain irrelevant and show near-Gaussian scaling and signatures of weak coupling. Moreover, a new equal weight condition is put forward to identify stable eigenvectors to all orders in the expansion. Similarities and differences with results from the Einstein-Hilbert approximation, $f(R)$ approximations, and $f(R,{\rm Ric}^2)$ models are highlighted and the relevance of findings for quantum gravity and the asymptotic safety conjecture is discussed.

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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