Quantum Horizon Tadpole and Emergence of a de Sitter Interior
Abstract
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.
Related
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- Evading the Swampland de Sitter Obstruction via Thermodynamic Duality-Induced Horizon Corrections in Unimodular Gravity
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- Real Part Emergence in Purely Imaginary Quasinormal Modes in Perturbed de Sitter Braneworlds
- Real part emergence in purely imaginary quasinormal modes in perturbed de Sitter braneworlds
BibTeX
@misc{chu2026quantum,
title = {{Quantum Horizon Tadpole and Emergence of a de Sitter Interior}},
author = {Chong-Sun Chu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.21178},
eprint = {2608.21178},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21178},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Horizon Tadpole and Emergence of a de Sitter Interior
AU - Chong-Sun Chu
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2608.21178
UR - https://arxiv.org/abs/2608.21178
AB - 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.
ER -