论文标题
小说4D爱因斯坦 - 加斯 - 鲍尼特重力的注释
A note on the novel 4D Einstein-Gauss-Bonnet gravity
论文作者
论文摘要
最近，Glavan和Lin [Phys。莱特牧师。 124，081301（2020）]通过重新缩放耦合$α\rightArrowα/（d-4）$，并在运动级别上占据限制$ d \ rightarrow 4 $ 4 $。尽管证明该处方会为特定对称性的某些空间带来非平凡的效果，但仍然神秘，并需要进行审查。确实，在较高的$ d $维度方程中，没有连续的方法可以采用限制$ d \ rightarrow 4 $，因为张量指数取决于时空维度并离散地表现。另一方面，如果与四维时空索引一起使用，则对应于高斯式项的贡献在运动方程中相同消失。该程序工作的必要条件（但可能不够）是，将四维时空嵌入到较高的$ d $ d $维时空中，以便在限制限制后可以正确解释后者中的方程。在本说明中，使用2D爱因斯坦重力，我们在应用[Phys中使用的方法时都会显示几个微妙之处。莱特牧师。 124，081301（2020）]。
Recently, a novel 4D Einstein-Gauss-Bonnet gravity has been proposed by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by rescaling the coupling $α\rightarrow α/(D-4)$ and taking the limit $D\rightarrow 4$ at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit $D\rightarrow 4$ in the higher $D$-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with four-dimensional spacetime indices the contribution corresponding to the Gauss-Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the four-dimensional spacetime into the higher $D$-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in [Phys. Rev. Lett. 124, 081301 (2020)].
