Nonrenormalization and naturalness in a class of scalar-tensor theories
Nonrenormalization and naturalness in a class of scalar-tensor theories
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一类标量张量理论中的非重整化和自然性
DOI：
10.1103/physrevd.87.085017
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发表时间：
2012
影响因子：
5
通讯作者：
D. Pirtskhalava
中科院分区：
文献类型：
--
作者：
C. Rham;G. Gabadadze;Lavinia Heisenberg;D. Pirtskhalava
我们研究了一类非线性标量张量理论中一些 4、7 和 10 维算子的重整化。这些理论在以下情况下是不变的：(a) 线性微分同胚，表示完全非线性作用的精确对称性，以及 (b) 标量场的全局场空间伽利略变换。拉格朗日包含一组上述维度的非拓扑相互作用项，我们证明它们在微扰理论中没有以任何阶重整化。我们还讨论了其他运算符的重整化，这些运算符可能由循环生成和/或接收循环校正，并确定它们相对于未重整化的运算符处于次领先的状态。有趣的是，这种标量张量理论出现在无鬼引力理论的某个高能极限中。人们可以利用高能极限的非重正化性质来估计整个理论中量子修正的幅度。我们表明，模型的三个自由参数（其中之一是引力子质量）的量子修正受到强烈抑制。特别是，我们证明了具有任意小的引力子质量在技术上是自然的。
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum corrections to the three free parameters of the model, one of them being the graviton mass, are strongly suppressed. In particular, we show that having an arbitrarily small graviton mass is technically natural.