arXiv 1507.086572015-07-30hep-thgr-qc

渐近安全性中重建问题的解

Solutions to the reconstruction problem in asymptotic safety

Tim R. Morris, Zoë H. Slade

备注：: 32 pages
DOI：: 10.1007/JHEP11(2015)094

摘要：

从有效平均动作的完全重正化轨迹开始（也称为红外截止勒让德有效作用量）$Γ_k$，我们明确地重建相应的裸作用量，以两种方式之一制定。第一步是根据$Γ_k$提供的顶点，通过树级展开构造相应的Wilson有效动作$S^k$。它形成了一个完美的裸动作，给出了相同的重新正规化的轨迹。一个裸露的行动与一些紫外线截止尺度$Λ$和红外线截止$k$必然产生一个有效的平均行动$Γ^Λ_k$取决于这两个截止，但如果已经计算的$S^Λ$使用，我们展示了如何$Γ^Λ_k$也可以计算$Γ_k$的树级扩展，以及$Γ^Λ_k\toΓ_k$作为$Λ\to\infty$。一路上，我们表明具有不同紫外截止曲线但对应于相同威尔逊有效作用量的勒让德有效作用量通过树级展开是相关的。所有这些展开都遵循勒让德变换关系，勒让德变换关系可以从$Γ^Λ_k$和$S^k$之间的原始勒让德变换关系导出。

英文摘要：

Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) $Γ_k$, we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action $S^k$ through a tree-level expansion in terms of the vertices provided by $Γ_k$. It forms a perfect bare action giving the same renormalised trajectory. A bare action with some ultraviolet cutoff scale $Λ$ and infrared cutoff $k$ necessarily produces an effective average action $Γ^Λ_k$ that depends on both cutoffs, but if the already computed $S^Λ$ is used, we show how $Γ^Λ_k$ can also be computed from $Γ_k$ by a tree-level expansion, and that $Γ^Λ_k\toΓ_k$ as $Λ\to\infty$. Along the way we show that Legendre effective actions with different UV cutoff profiles, but which correspond to the same Wilsonian effective action, are related through tree-level expansions. All these expansions follow from Legendre transform relationships that can be derived from the original one between $Γ^Λ_k$ and $S^k$.

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