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arXiv 2006.16682hep-thgr-qc
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微扰论中二阶量子引力的连续极限

The continuum limit of quantum gravity at second order in perturbation theory

Matthew Kellett, Alex Mitchell, Tim R. Morris

摘要:

我们证明了基于Einstein-Hilbert作用量的微扰量子引力具有一个新的连续极限。重正化的轨迹从高斯不动点沿(边缘)相关的方向,但进入的同形不变子空间,只有远远低于动态生成的规模。我们证明了,对于二阶微扰理论的纯量子引力,当宇宙学常数为零时,结果与标准量子化的计算结果相同。虽然这种情况下是重正化在二阶运动的原因,我们发现的结构工程一般。一种可能性是,引力有一个真正一致的连续极限,即使它有无限多个耦合。然而,我们也提出了一种可能的非微扰机制,根据这些流动方程的抛物性质,这将固定所有高阶耦合的牛顿常数和宇宙学常数。

英文摘要:

We show that perturbative quantum gravity based on the Einstein-Hilbert action, has a novel continuum limit. The renormalized trajectory emanates from the Gaussian fixed point along (marginally) relevant directions but enters the diffeomorphism invariant subspace only well below a dynamically generated scale. We show that for pure quantum gravity to second order in perturbation theory, and with vanishing cosmological constant, the result is the same as computed in the standard quantisation. Although this case is renormalizable at second order for kinematic reasons, the structure we uncover works in general. One possibility is that gravity has a genuine consistent continuum limit even though it has an infinite number couplings. However we also suggest a possible non-perturbative mechanism, based on the parabolic properties of these flow equations, which would fix all higher order couplings in terms of Newton's constant and the cosmological constant.

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