QEG的R^2 phase-diagram及其谱维数
The R^2 phase-diagram of QEG and its spectral dimension
摘要：
在引力渐近安全程序中，详细分析了三维和四维时空中R^2截断的RG流。特别是，我们构建RG轨迹，从非高斯UV不动点发出，并拥有长期的经典制度，其中有效的平均行动是很好地近似经典的爱因斯坦-希尔伯特行动。作为一个应用程序，我们研究的有效QEG时空的谱维数从这些轨迹，建立的多重分形时空的图片下截断的理论空间的扩展是强大的。我们证明了常谱维数的区域既可以归因于RG不动点的普适特征，也可以归因于β函数中的奇异轨迹.
英文摘要：
Within the gravitational asymptotic safety program, the RG flow of the R^2 truncation in three and four spacetime dimensions is analyzed in detail. In particular, we construct RG trajectories which emanate from the non-Gaussian UV fixed point and possess long classical regimes where the effective average action is well approximated by the classical Einstein-Hilbert action. As an application we study the spectral dimension of the effective QEG spacetimes resulting from these trajectories, establishing that the picture of a multi-fractal spacetime is robust under the extension of the truncated theory space. We demonstrate that regimes of constant spectral dimensions can either be attributed to universal features of RG fixed points or singular loci in the βfunctions.
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