论文标题
量子重力的固定点和紫外线临界表面的尺寸
Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
论文作者
论文摘要
我们研究了使用功能重量级化组的一般相对性较高曲率扩展的量子效应。新的流程方程是针对涉及RICCI标量，RICCI张量和Riemann Tensor相互作用的通用类别的一般类别得出的。我们的方法用于测试渐近安全构量的量子重力，并通过多项式riemann张量相互作用的形式的相互作用，$ \ sim \ sim \ int \ int \ sqrt {g} \，（r_ {μνστ} r \ cdot（r_ {μνστ} r^{μνστ}）^n $及其功能。通过组合高阶多项式近似值，padé重新启动和完整的数值集成来鉴定相互作用的固定点，特征值光谱中的差距，运动量子方程和DE Sitter溶液的相互作用。最值得注意的是，我们发现量子诱导的缩放尺寸的变化会导致四维紫外线临界表面。越来越高的相互作用仍然无关紧要，并且显示出近高斯的缩放和弱耦合的特征。此外，提出了新的同等重量条件，以确定扩展中所有订单的稳定特征向量。强调了与爱因斯坦 - 希尔伯特（Einstein-Hilbert）近似，$ f（r）$近似和$ f（r，{\ rm ric}^2）$模型的相似性和差异。
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.
