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arXiv 2004.06475hep-thgr-qc
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微扰论中一阶量子引力的连续极限

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

Alex Mitchell, Tim R. Morris

摘要:

度规的共形因子的威尔逊重整化群(RG)性质被一个错误符号的动力学项所深刻改变。其结果是一个新的微扰连续极限的量子引力,但在$\hbar$的非微扰。重整化轨迹的紫外线部分位于非同形不变子空间之外,仅在红外线中进入该子空间,低于动态生成的幅度抑制尺度。相互作用的共形因子的系数函数,其形式被确定的RG。在紫外线中,系数函数由无穷多个潜在的耦合参数化。适当地选择这些耦合,系数函数在进入非同态不变子空间时平凡化。在这里,动态生成的有效的同构耦合出现,包括牛顿常数。根据勒让德有效作用量,我们建立了一阶的连续极限,刻画了这类系数函数的最一般形式,以验证其普适性。

英文摘要:

The Wilsonian renormalization group (RG) properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity, which is however non-perturbative in $\hbar$. The ultraviolet part of the renormalized trajectory lies outside the diffeomorphism invariant subspace, entering this subspace only in the infrared, below a dynamically generated amplitude suppression scale. Interactions are dressed with coefficient functions of the conformal factor, their form being determined by the RG. In the ultraviolet, the coefficient functions are parametrised by an infinite number of underlying couplings. Choosing these couplings appropriately, the coefficient functions trivialise on entering the diffeomorphism invariant subspace. Here, dynamically generated effective diffeomorphism couplings emerge, including Newton's constant. In terms of the Legendre effective action, we establish the continuum limit to first order, characterising the most general form of such coefficient functions so as to verify universality.

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