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arXiv 1809.04671hep-th
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低阶RG流动方程的高阶导数修正

Higher Derivative Corrections to Lower Order RG Flow Equations

S. P. de Alwis

备注：
Clarifying comments added, minor corrections, references added typos corrected, 12 pages
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摘要：

我们表明，RG流方程的宇宙学常数（CC）接收的贡献（除了那些来自CC的爱因斯坦-希尔伯特项和$R^{2}$和$R_{μν}^{2}$条款），只有两个权力的曲率，但也有权力的协变导数，在威尔逊有效作用量。在纯引力中，我们的论证意味着，仅仅考虑$f(R)$理论将忽略由诸如$"R"\square^{n}"R",\,n=0,1,2,\ldots$之类的项引起的这种效应。我们也期望对Einstein-Hilbert项的流动方程有类似的贡献。最后，我们认为，来自曲率平方项的扰动鬼的行动实际上是虚假的，因为它们是在截止尺度，可以删除（截止依赖）字段重新定义。

英文摘要：

We show that the RG flow equation for the cosmological constant (CC) receives contributions (in addition to those coming from the CC the Einstein-Hilbert term and $R^{2}$ and $R_{μν}^{2}$ terms) only from terms with just two powers of curvature, but having also powers of the covariant derivative, in the Wilsonian effective action. In pure gravity our argument implies that just considering $f(R)$ theories will miss this effect which arises from terms such as $"R"\square^{n}"R",\,n=0,1,2,\ldots$. We expect similar contributions for the flow equation of the Einstein-Hilbert term as well. Finally we argue that the perturbative ghosts coming from curvature squared terms in the action are in fact spurious since they are at the cutoff scale and can be removed by (cutoff dependent) field redefinitions.

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