二维p进空间上的一种引力理论及p进AdS/CFT猜想

中文摘要 AI 辅助

借助高维嵌入方法，结合对距离、测度与曲率的研究，我们在p进数域上的二维空间构建了一种引力理论。在得到最终引力理论前，我们补充了基于现有文献的部分计算，并通过与实数情形的对比论证该引力理论的合理性，例如德西特（dS）空间、反德西特（AdS）空间与欧氏空间的曲率应分别为正、负、零。最后，我们提出两个猜想：（1）p进AdS/CFT可在任意空间中计算，不仅限于p进AdS空间（pAdS），且结果本质一致；（2）p进CFT本质唯一。

英文摘要

By means of a higher-dimensional embedding approach, together with the study of distance, measure, and curvature, we construct a gravitational theory on the two-dimensional space over $p$-adic numbers. Before constructing this gravitational theory, we provide supplementary calculations based on existing literature and justify the validity of the gravitational theory by comparison with the real-number case, for instance, the curvatures of de Sitter(dS), anti-de Sitter(AdS), and Euclidean space should be positive, negative, and zero, respectively. Finally, as an example on the gravity side of the $p$-adic AdS$_2$/CFT$_1$, we present the action for a scalar field coupled to gravity.

补充信息

备注

10 pages, 7 figures, 2 tables. Dimensional analysis has been rigorously treated, the one-dimensional examples have been removed, a more general definition of curvature has been introduced, the coupling between gravity and a scalar field has been incorporated, two conjectural statements have been deleted, minor errors and typos have been corrected