论文标题
在扰动理论中，共形部门的连续性极限
The continuum limit of the conformal sector at second order in perturbation theory
论文作者
论文摘要
最近，已经提出了一种新型的量子重力扰动连续性极限，并证明是一阶起作用的。每种交互单元$σ$均穿着系数函数$ f^σ_λ（φ）$的$ f^σ_λ$，$φ$。每个系数函数都通过无限数量的基础耦合来参数，并且具有特征性振幅抑制刻度的大$φ$衰减，可以选择为共同值，$λ_\ text {p} $。尽管该理论在耦合中是扰动的，但在$ \ hbar $中是非扰动的。在扰动理论的二阶情况下，必须对所有旋律Feynman图进行总和以获得特定的积分。我们证明，它导致了一个定义明确的重新归一化轨迹，因此可以连续限制，前提是通过以任意的截止量表$λ=μ$启动来解决，该范围在$ 0 <μ<aλ_\aλ_\ text {p text {p} $（$ a $ a $ a $ a $某些非额外号码）。如果$μ$位于此范围以上，则在达到物理极限之前，所得的系数函数将变得单数，并且流量停止。在这方面，必须添加一个举止良好的互补解决方案，其中包含由一阶相互作用独特确定的无关耦合，并重新归一化的相关耦合。即使某些无关紧要的耦合在限制$λ_\ text {p} \ to \ infty $中的差异，但可以选择基础相关耦合的域，以便在此限制中恢复了差异不变，在此限制中将恢复，在此限制中，基础耦合消失在哪里可以替代有效的diffefemorphiant coutriantcouriantcouriantcouriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant cououriant couount。
Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial $σ$ is dressed with a coefficient function $f^σ_Λ(φ)$ of the conformal factor field, $φ$. Each coefficient function is parametrised by an infinite number of underlying couplings, and decays at large $φ$ with a characteristic amplitude suppression scale which can be chosen to be at a common value, $Λ_\text{p}$. Although the theory is perturbative in couplings it is non-perturbative in $\hbar$. At second order in perturbation theory, one must sum over all melonic Feynman diagrams to obtain the particular integral. We show that it leads to a well defined renormalized trajectory and thus continuum limit, provided it is solved by starting at an arbitrary cutoff scale $Λ=μ$ which lies in the range $0<μ<aΛ_\text{p}$ ($a$ some non-universal number). If $μ$ lies above this range the resulting coefficient functions become singular, and the flow ceases to exist, before the physical limit is reached. To this one must add a well-behaved complementary solution, containing irrelevant couplings determined uniquely by the first-order interactions, and renormalized relevant couplings. Even though some irrelevant couplings diverge in the limit $Λ_\text{p}\to\infty$, domains for the underlying relevant couplings can be chosen such that diffeomorphism invariance will be recovered in this limit, and where the underlying couplings disappear to be replaced by effective diffeomorphism invariant couplings.
