Spectral geometry as a probe of quantum spacetime
Spectral geometry as a probe of quantum spacetime
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DOI：
10.1103/physrevd.80.124036
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发表时间：
2009-12-01
影响因子：
5
通讯作者：
Henson, Joe
中科院分区：
文献类型：
--
作者：
Benedetti, Dario;Henson, Joe
采用标准的结果，从谱几何，我们提供了强有力的证据表明，在经典极限的三维因果动力学三角形的基态是德西特时空。这一结果是通过测量这些模型定义的几何集合的光谱维度的期望值，并将其大尺度行为与球体（欧几里得德西特）的行为进行比较而获得的。从相同的测量中，我们还能够证实在这种和其他量子引力方法中观察到的动力学维度减少现象--这是第一次针对三维因果动力学三角测量进行这样的研究。在这种情况下，我们找到的谱维数的短尺度极限值约为2。我们评论的相关性，这些结果的比较，渐近安全和Horcava-Lifshitz引力，量子引力的其他方法。
Employing standard results from spectral geometry, we provide strong evidence that in the classical limit the ground state of three-dimensional causal dynamical triangulations is de Sitter spacetime. This result is obtained by measuring the expectation value of the spectral dimension on the ensemble of geometries defined by these models, and comparing its large-scale behavior to that of a sphere (Euclidean de Sitter). From the same measurement we are also able to confirm the phenomenon of dynamical dimensional reduction observed in this and other approaches to quantum gravity-the first time this has been done for three-dimensional causal dynamical triangulations. In this case, the value for the short-scale limit of the spectral dimension that we find is approximately 2. We comment on the relevance of these results for the comparison to asymptotic safety and Horcava-Lifshitz gravity, among other approaches to quantum gravity.