AI 中文总结
该研究在大N矩阵量子力学框架下，证明了模糊球黑洞视界的微扰稳定性，揭示了低角动量模式的量子稳定效应与高角动量模式的经典稳定效应在L~√N处相当，且该区域也主导隧穿过程。
AI 中文摘要
我们在文献[Chu:2024qil]的大N矩阵量子力学框架下，证明了模糊球黑洞视界的微扰稳定性。大N计数显示，涨落谱的领头阶量子修正为平面玻色子单圈贡献，而高阶玻色子效应和领头阶费米子单圈贡献在参数上被抑制。经典谱包含一个快子(1,2)模式和一个边缘(2,3)模式；我们证明两者均获得正的量子曲率并被稳定化。对于一般谱，我们发现海森矩阵的因式分解结构控制着领头阶量子曲率并使其非负。量子效应主导了一般低角动量模式的稳定化，而经典曲率在高角动量时占主导。两种效应在交叉区域L~√N处相当，此时必须同时保留两者。在有限N数值测试支持的光滑性和非饱和假设下，我们因此证明了足够大但有限N时量子涨落谱的正定性。这种局部曲率稳定性与非微扰单极子隧穿兼容。有趣的是，相同的L~√N介观角动量范围也主导隧穿过程，这表明黑洞视界量子动力学中存在一个特殊的红外-紫外交叉区域。
英文摘要
We establish the perturbative stability of the fuzzy-sphere black-hole horizon in the large-$N$ matrix quantum mechanics of \cite{Chu:2024qil}. Large-$N$ counting shows that the leading quantum correction to the fluctuation spectrum is the planar bosonic one-loop contribution, while higher-loop bosonic effects and the leading fermionic one-loop contribution are parametrically suppressed. The classical spectrum contains a tachyonic $(1,2)$ mode and a marginal $(2,3)$ mode; we show that both acquire positive quantum curvature and are stabilized. For the general spectrum, we find that a factorization structure of the Hessian controls the leading quantum curvature and renders it non-negative. Quantum effects dominate the stabilization of generic low-angular-momentum modes, whereas classical curvature dominates at high angular momentum. The two effects become comparable in the crossover regime $L \sim \sqrt{N}$, where both must be retained. Under smoothness and non-saturation assumptions supported by finite-$N$ numerical tests, positivity of the quantum fluctuation spectrum is thus established for sufficiently large but finite $N$. This local curvature stability is compatible with non-perturbative monopole tunneling. Intriguingly, the same $L\sim\sqrt{N}$ mesoscopic angular momentum range also dominates the tunneling process, suggesting a distinguished IR--UV crossover regime in the quantum dynamics of the black-hole horizon.
Comments54 pages. no figure
