arXiv 2005.122922020-05hep-th

$D\to4$ Einstein-Gauss-Bonnet引力及其他

$D\to4$ Einstein-Gauss-Bonnet Gravity and Beyond

Damien A. Easson, Tucker Manton, Andrew Svesko

备注：: 12 pages, references added, published in JCAP, https://doi.org/10.1088/1475-7516/2020/10/026
DOI：: 10.1088/1475-7516/2020/10/026

摘要：

通过重新标度高斯-博内耦合常数，可以构造一个四维时空中的爱因斯坦-高斯-博内引力的“新”纯理论，这似乎避开了洛夫洛克定理。然而，最近，这个模型的适定性受到了质疑。在这里，我们应用“维数正则化”技术，首先使用的曼和罗斯写下广义相对论的$D\to2$限制，纯爱因斯坦-高斯-邦纳引力的情况下。由此产生的四维作用量是一种特殊的霍恩代斯基引力理论，与通过卡鲁扎-克莱因在平坦内部空间上的约化发现的结果相匹配。一些宇宙学的解决方案，这四维理论进行检查。我们进一步调整的技术，以更高的曲率洛夫洛克引力理论，以及一个低能量的有效弦作用与$α'$校正。关于$α'$校正的弦作用量的$D\to4$极限，我们发现我们还必须重新标度介子，使其在四维中具有非奇异作用量。有趣的是，当共形重标度$Φ$被解释为另一个引力子时，正则化弦作用量似乎是协变多伽利略引力理论的一个特例。

英文摘要：

A `novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant, seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of this model has been called into question. Here we apply a `dimensional regularization' technique, first used by Mann and Ross to write down a $D\to2$ limit of general relativity, to the case of pure Einstein-Gauss-Bonnet gravity. The resulting four-dimensional action is a particular Horndeski theory of gravity matching the result found via a Kaluza-Klein reduction over a flat internal space. Some cosmological solutions of this four-dimensional theory are examined. We further adapt the technique to higher curvature Lovelock theories of gravity, as well as a low-energy effective string action with an $α'$ correction. With respect to the $D\to4$ limit of the $α'$-corrected string action, we find we must also rescale the dilaton to have a non-singular action in four dimensions. Interestingly, when the conformal rescaling $Φ$ is interpreted as another dilaton, the regularized string action appears to be a special case of a covariant multi-Galileon theory of gravity.

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