具有高曲率项的软破缺共形对称
Softly broken conformal symmetry with higher curvature terms
摘要：
在标量耦合引力模型中，在标量场的质量重整化中出现的二次发散反项必须继承引力相互作用引起的修正。在这项工作中，我们已经明确地证明，有没有这样的修正引力起源的平方发散的质量计数器条款。无论引力相互作用的性质如何，这一陈述都是正确的，即，引力是由广义相对论还是f（R）理论描述的。有趣的是，标量耦合引力系统的单圈有效作用量也是行为良好的\emph{if and only if}，$f(R)$理论没有鬼。特别是，在f（R）理论的背景下导出的结果被证明是在严格的协议与相应的结果来自等价的标量张量表示。我们的分析表明，标量场的质量可以始终保持小于一些紫外线（UV）截止尺度，是独立的重力理论的性质，这可能涉及更高的曲率修正的诱人的可能性。只要物质场和引力理论能够一致地嵌入到普朗克尺度下的UV完备理论中，所有这些都是正确的。
英文摘要：
In a scalar-coupled-gravity model, the quadratically divergent counter term appearing in the mass renormalization of the scalar fields must inherit corrections arising out of gravitational interactions. In this work we have explicitly demonstrated that there are no such corrections of gravitational origin to the quadratic divergences in the mass counter terms. This statement holds true irrespective of the nature of the gravitational interaction, i.e., whether gravity is described by general relativity or f(R) theory. Interestingly, it also turns out that the one loop effective action of scalar-coupled-gravity system will be well-behaved \emph{if and only if} the $f(R)$ theory is free from ghosts. In particular, the results derived in the context of f(R) theory are shown to be in exact agreement with the corresponding results derived from the equivalent scalar-tensor representation. Our analysis suggests the tantalizing possibility that the masses of the scalar fields can be consistently kept smaller than some Ultra Violet (UV) cutoff scale and is independent of the nature of the gravity theory, which may involve higher curvature corrections. All these will be true provided the matter fields and the gravity theory can be embedded consistently into a UV complete theory at the Planck scale.
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