标题： 本质量子爱因斯坦引力 显示英文标题

标题： Essential Quantum Einstein Gravity

摘要： 研究了量子引力的非微扰重整化，允许度规沿重正化群（RG）流重新参数化，使得只有本质耦合常数被重整化。 这使我们能够识别一个保证是幺正的量子引力普适类，因为物理自由度是广义相对论中的自由度，没有物质且宇宙学常数为零。 考虑所有具有至多四个导数的微分同胚不变算符，在与线性化的爱因斯坦-希尔伯特作用量相关的高斯红外不动点处，只有牛顿常数是本质的。 然后可以在该普适类的重正化群流中，将其它非本质耦合固定为其在高斯不动点处的取值。 在紫外区，与相互作用Reuter不动点相关的牛顿常数对应的β函数消失。 Reuter不动点的性质在爱因斯坦-希尔伯特近似和包括流方程中所有微分同胚不变四阶导数项的近似之间是稳定的。 我们的结果表明，Reuter不动点处唯一相关的是牛顿常数这一本质耦合。 因此，我们推测，在物质不存在且尤其在预言宇宙学常数为零的情况下，量子爱因斯坦引力——即广义相对论在渐近安全性场景下的紫外完备理论——没有自由参数。 显示英文摘要

摘要： The non-perturbative renormalisation of quantum gravity is investigated allowing for the metric to be reparameterised along the RG flow, such that only the essential couplings constants are renormalised. This allows us to identify a universality class of quantum gravity which is guaranteed to be unitary, since the physical degrees of freedom are those of general relativity without matter and with a vanishing cosmological constant. Considering all diffeomorphism invariant operators with up to four derivatives, only Newton's constant is essential at the Gaussian infrared fixed point associated to the linearised Einstein--Hilbert action. The other inessential couplings can then be fixed to the values they take at the Gaussian fixed point along the RG flow within this universality class. In the ultraviolet, the corresponding beta function for Newton's constant vanishes at the interacting Reuter fixed point. The properties of the Reuter fixed point are stable between the Einstein--Hilbert approximation and the approximation including all diffeomorphism invariant four derivative terms in the flow equation. Our results suggest that Newton's constant is the only relevant essential coupling at the Reuter fixed point. Therefore, we conjecture that quantum Einstein gravity, the ultraviolet completion of Einstein's theory of general relativity in the asymptotic safety scenario, has no free parameters in the absence of matter and in particular predicts a vanishing cosmological constant.