论文标题
渐近安全希尔伯特 - 帕拉蒂尼重力
Asymptotically Safe Hilbert-Palatini Gravity in an On-Shell Reduction Scheme
论文作者
论文摘要
我们研究了希尔伯特 - 帕拉蒂尼重力的重新归一化流动至最低的非平凡秩序。我们发现，基于与量子爱因斯坦重力的路透社固定点相似的紫外线固定点的存在，证明了渐近安全的高能完成。为了管理按公制和连接的大量独立自由度量化的量化，我们使用壳体减少方案：为此，我们按以前顺序使用运动方程后在给定的顺序下定量所有自由度以外的自由度。通过这种方式，与爱因斯坦重力相比，我们可以直接地跟踪量化希尔伯特 - 帕蒂尼重力的差异。达到最低的非平凡阶，差异是通过额外的Abelian仪表场的波动来参数化的。 Hilbert-Palatini重力的紫外线固定点的临界特性与Reuter固定点相似，该点发生在较小的牛顿耦合处，并显示出更稳定的高阶指数。
We study the renormalization flow of Hilbert-Palatini gravity to lowest non-trivial order. We find evidence for an asymptotically safe high-energy completion based on the existence of an ultraviolet fixed point similar to the Reuter fixed point of quantum Einstein gravity. In order to manage the quantization of the large number of independent degrees of freedom in terms of the metric as well as the connection, we use an on-shell reduction scheme: for this, we quantize all degrees of freedom beyond Einstein gravity at a given order that remain after using the equations of motion at the preceding order. In this way, we can straightforwardly keep track of the differences emerging from quantizing Hilbert-Palatini gravity in comparison with Einstein gravity. To lowest non-trivial order, the difference is parametrized by fluctuations of an additional abelian gauge field. The critical properties of the ultraviolet fixed point of Hilbert-Palatini gravity are similar to those of the Reuter fixed point, occurring at a smaller Newton coupling and exhibiting more stable higher order exponents.
