Maldacena-Milekhin-Popov 虫洞的极向度规/轴向导场扰动

中文摘要 AI 辅助

我们研究 Maldacena-Milekhin-Popov (MMP) 可穿越虫洞的线性扰动。在磁荷背景上，极向度规扰动与轴向导场扰动耦合。我们处理这一扇区并将其约化为两个 Zerilli-Moncrief 类型的耦合主方程。虫洞有两个区域。在口部，几何是近极端的磁 Reissner-Nordstrom 黑洞，没有量子源。在喉部，最低朗道能级的带电费米子的 Casimir 能量维持虫洞张开。我们证明，喉部方程仅在费米子响应扰动时自洽，该响应由二维共形反常精确计算，包含 MMP 忽略的包括迹部分的完整应力张量。这种响应必须伴随费米子诱导的霍尔电流。包含这两种效应后，线性化的 Bianchi 恒等式在费米子反作用 α 的一阶成立。从费米子有效作用量推导霍尔电流则需要一个系数为 c/48π 的 Euler 项，它成为磁通与曲率之间的耦合，类似于 Wen-Zee 项。在 α=0 时，喉部是精确的 AdS₂×S²，模式解耦为两个 Pöschl-Teller 问题，质量分别为 l(l-1) 和 (l+1)(l+2)，频率间隔为 1/ℓ。我们给出 O(α) 修正的闭式表达式。它们混合两种模式并依赖于频率，且在重叠区域与口部匹配。势的对称部分在整个虫洞中为正，排除了纯指数增长。修正降低了正常频率并分裂两种模式共享的能级，在 α 一阶时产生实频移。在此阶，该扇区对于 l≥2 没有增长模式。

英文摘要

We study linear perturbations of the Maldacena-Milekhin-Popov (MMP) traversable wormhole. On a magnetically charged background, polar metric perturbations couple to axial perturbations of the gauge field. We treat this sector and reduce it to two coupled master equations of Zerilli-Moncrief type. The wormhole has two regions. In the mouths the geometry is a nearly extremal magnetic Reissner-Nordstrom black hole with no quantum source. In the throat the Casimir energy of the lowest Landau level of charged fermions holds the wormhole open. We show that the throat equations are consistent only if the fermions respond to the perturbation, computed exactly from the two-dimensional conformal anomaly with the full stress tensor including the trace part that MMP discard. This response must be accompanied by an induced Hall current of the fermions. With both effects included, the linearised Bianchi identities hold at first order in the fermionic backreaction $α$. Deriving the Hall current from the fermion effective action instead requires an Euler term with coefficient $c/48π$, which becomes a coupling between magnetic flux and curvature similar to a Wen-Zee term. At $α=0$ the throat is exact AdS$_2\times S^2$ and the modes decouple into two Poschl-Teller problems with masses $l(l-1)$ and $(l+1)(l+2)$, with levels spaced by $1/\ell$ in frequency. We give the $O(α)$ corrections in closed form. They mix the two modes and depend on frequency, and match the mouths in the overlap region. The symmetric part of the potential is positive throughout the wormhole, excluding purely exponential growth. The corrections lower the normal frequencies and split the levels shared by the two modes, with real shifts at first order in $α$. This sector has no growing mode for $l\ge2$ at this order.

发表机构

• Presidency University（总统大学）

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77 pages