论文标题
高衍生引力的一环差异
One-loop divergences in higher-derivative gravity
论文作者
论文摘要
我们对高导数重力理论中的一环差异进行了回顾。我们首先在任意背景下在量子波动中进行双线性扩展，引入更高衍生的量规固定，并表明除了那些天真的预期之外，更高衍生的量规固定还必须具有幽灵。我们给出了此类理论中一环差异的一般公式，并为具有二次曲率项的理论给出了明确的结果。在此计算中，我们需要四源性最小运算符和两衍生的非微小载体算子的热内核系数，这是总结的。我们还讨论了重新归一化组中的β函数，并表明无量纲耦合是渐近的。该计算还扩展到了$ r $和$ r_ {μν}^2 $的任意功能的理论。我们表明，结果与壳上的度量参数化无关。
We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that higher-derivative gauge fixing must have ghosts in addition to those naively expected. We give general formulae for the one-loop divergences in such theories, and give explicit results for theories with quadratic curvature terms. In this calculation, we need the heat kernel coefficients for the four-derivative minimal operators and two-derivative nonminimal vector operators, which are summarized. We also discuss the beta functions in the renormalization group, and show that the dimensionless couplings are asymptotically free. The calculation is also extended to the theories with arbitrary functions of $R$ and $R_{μν}^2$. We show that the result is independent of metric parametrization and gauge on shell.
