量子视界蝌蚪与德西特内部的涌现
Quantum Horizon Tadpole and Emergence of a de Sitter Interior
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中文总结 AI 辅助
该研究基于模糊球面的量子稳定性与矩阵几何的蝌蚪，探讨视界孤立时的收缩效应，耦合引力后通过广义相对论衔接条件选出纯德西特空间，确定了德西特内部与史瓦西外部的大N焊接关系并讨论宇宙学意义。
中文摘要 AI 辅助
在近期的一篇论文[Chu:2026dhx]中，模糊球面在大但有限的N下的量子稳定性得到了证实，此外还识别出矩阵几何标度涨落模式存在一个蝌蚪。本文表明，若视界保持孤立，该蝌蚪会产生正表面张力并使球面收缩；但当视界与引力耦合时，蝌蚪要求体几何根据广义相对论的衔接条件调整，在假设静态、球对称且无奇点的真空内部的情况下，会选出纯德西特空间，该匹配还确定了德西特内部时间与外部史瓦西时间之间引人关注的大N焊接关系，文中讨论了其潜在的宇宙学意义。
英文摘要
In a recent paper \cite{Chu:2026dhx}, the quantum stability of the fuzzy sphere was established at large but finite $N$, where a tadpole was also identified for the scaling fluctuation mode of the matrix geometry. Here we show that this tadpole generates a positive area-conjugate microscopic response, which in isolation energetically favors contraction of the fuzzy sphere. However, when the horizon is coupled to gravity, the tadpole requires the bulk geometry to adjust according to the junction condition of general relativity. Taking the exterior geometry to be Schwarzschild, we show that the junction condition requires a positive interior cosmological constant. Imposing a static, spherically symmetric, regular vacuum interior then selects pure de Sitter space. The matching further determines a soldering relation between the interior de Sitter time and the exterior Schwarzschild time, with a relative lapse growing as $C = O(N)$. We also propose a matrix realization of the de Sitter interior in which fuzzy-sphere representation sizes determine the angular geometry while condensates of off-diagonal link fields determine the emergent radial metric. This provides a concrete consistency test for spacetime emergence from the matrix degrees of freedom. Potential cosmological implications are discussed.
发表机构
- National Tsing-Hua University（国立清华大学）
- National Center for Theoretical Sciences（国家理论科学中心）
机构由 AI 辅助整理，请以论文原文为准。
