从黑洞纠缠中读取拓扑毛发
Reading Topological Hair from Black-Hole Entanglement
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中文总结 AI 辅助
本文通过分离应力能量与拓扑通道，在BTZ黑洞上利用Wilson-线程反射矩和Chern-Simons完备化，实现了拓扑毛发与引力dressing的区分，并计算了相关几何可观测量。
中文摘要 AI 辅助
黑洞毛发可以通过局部应力-能量以及经典度规不可见的拓扑信息影响边界混合态纠缠。我们针对非旋转BTZ黑洞上的Nielsen-Olesen涡旋分离了这些通道。一个超选择定理表明，Shannon扇区熵在Markov间隙中抵消，而热$U(1)_k$ CFT中标准的$U(1)$对称分辨反射熵在领头阶是等分的，排除了不平衡分辨间隙中的普遍$\log|n|$项。因此，我们在与紧致涡旋通量类耦合的探针$U(1)_k$ Chern-Simons完备化中定义了Wilson-线程反射矩。在链接数为$\nu$的反射-副本扇区中，其归一化相位为$2\pi\kappa pn\nu/k$，其中$\kappa\in\mathbb Z$是混合拓扑耦合；对于$\gcd(\kappa\nu,k)=1$，离散傅里叶变换重构$n\bmod k$。RT连通性转变切换指定的链接轮廓的开或关，而独立尺度$\ell_\star r_+/L^2=1.128378\ldots$决定了该转变的涡旋诱导移动方向。带电矩模量和普通Markov间隙保持为几何可观测量，并从具有完整一阶变分核（包括纠缠楔横截面端点运动）的视界锚定Einstein-Abelian-Higgs解计算。这种相位和模量分离区分了拓扑毛发与引力 dressing，而不赋予无根据的绕数依赖熵。
英文摘要
Black-hole hair can affect boundary mixed-state entanglement through local stress-energy and through topological information invisible to the classical metric. We separate these channels for a Nielsen--Olesen vortex on a nonrotating BTZ black hole. A superselection theorem shows that Shannon sector entropy cancels from the Markov gap, while standard $U(1)$ symmetry-resolved reflected entropy in a thermal $U(1)_k$ CFT is equipartitioned at leading order, excluding a universal $\log|n|$ term in the imbalance-resolved gap. We therefore define a Wilson-threaded reflected moment in a probe $U(1)_k$ Chern--Simons completion coupled to the compact vortex-flux class. In a reflected-replica sector with linking number $ν$, its normalised phase is $2πκpnν/k$, where $κ\in\mathbb Z$ is the mixed topological coupling; for $\gcd(κν,k)=1$, a discrete Fourier transform reconstructs $n\bmod k$. The RT connectivity transition switches the specified linked contour on or off, whereas the independent scale $\ell_\star r_+/L^2=1.128378\ldots$ determines the direction of the vortex-induced shift of that transition. The charged-moment modulus and the ordinary Markov gap remain geometric observables and are computed from a horizon-anchored Einstein-Abelian-Higgs solution with a complete first-variation kernel including the motion of the entanglement-wedge cross-section endpoints. This phase and modulus separation distinguishes topological hair from gravitational dressing without assigning an unsupported winding-dependent entropy.
发表机构
- E.ON Digital Technology（E.ON数字技术）
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