[论文解读] The Gravity of Dark Vortices: Effective Field Theory for Branes and Strings Carrying Localized Flux

C. P. Burgess, Ross Diener+1 more|arXiv (Cornell University)|Jun 26, 2015

Cosmology and Gravitation Theories参考文献 31被引用 5

一句话总结

本文通过引入内部与外部 U(1) 规范场之间的非对角动能混合，构建了暗涡旋——即携带局域磁通并同时渗透到体空间的宇宙弦或膜——的有效场论。关键结果是，张力、缺陷角和弦上曲率等引力可观测量仅依赖于低能参数（张力与磁通），而不依赖于微观细节；膜局域磁通不产生引力，仅以与磁场无关的方式修正张力。

ABSTRACT

A Nielsen-Olesen vortex usually sits in an environment that expels the flux that is confined to the vortex, so flux is not present both inside and outside. We construct vortices for which this is not true, where the flux carried by the vortex also permeates the `bulk' far from the vortex. The idea is to mix the vortex's internal gauge flux with an external flux using off-diagonal kinetic mixing. Such `dark' vortices could play a phenomenological role in models with both cosmic strings and a dark gauge sector. When coupled to gravity they also provide explicit ultra-violet completions for codimension-two brane-localized flux, which arises in extra-dimensional models when the same flux that stabilizes extra-dimensional size is also localized on space-filling branes situated around the extra dimensions. We derive simple formulae for observables such as defect angle, tension, localized flux and on-vortex curvature when coupled to gravity, and show how all of these are insensitive to much of the microscopic details of the solutions, and are instead largely dictated by low-energy quantities. We derive the required effective description in terms of a world-sheet brane action, and derive the matching conditions for its couplings. We consider the case where the dimensions transverse to the bulk compactify, and determine how the on- and off-vortex curvatures and other bulk features depend on the vortex properties. We find that the brane-localized flux does not gravitate, but just renormalizes the tension in a magnetic-field independent way. The existence of an explicit UV completion puts the effective description of these models on a more precise footing, verifying that brane-localized flux can be consistent with sensible UV physics and resolving some apparent paradoxes that can arise with a naive (but commonly used) delta-function treatment of the brane's localization within the bulk.

研究动机与目标

• 构建一个包含内部磁通并可通过动能混合将外部磁通渗透到体空间的涡旋的紫外完备有效场论。
• 解决在额外维模型中对膜局域磁通使用狄拉克δ函数处理时存在的不一致性。
• 推导仅依赖于低能参数的引力可观测量（张力、缺陷角、曲率）的通用公式。
• 阐明膜局域磁通如何影响几何结构而不直接贡献于引力，与直观预期相反。
• 为暗光子模型以及具有磁通稳定性的共维数为二的膜世界情景提供一致的框架。

提出的方法

• 推导包含张力与磁通耦合主导项的世界膜膜作用量：$ S_b = -T_b \int \omega + \zeta_b \int \star A + \cdots $。
• 利用非对角动能混合将涡旋的内部规范场与外部 U(1) 场耦合，使磁通能够延伸至体空间。
• 在具有紧致横向维度的高维引力中构造显式解，求解带有局域源的爱因斯坦方程。
• 进行导数展开以识别主导引力响应，将张力与磁通分离为主要参数。
• 推导膜耦合的匹配条件，并在翘曲紧致化中计算弦上与弦外的曲率。
• 分析小翘曲极限，通过坐标变换至角变量，推导度规分量的修正。

实验结果

研究问题

• RQ1 当涡旋同时携带内部磁通并使外部磁通渗透到体空间时，其引力反作用如何变化？
• RQ2 尽管磁通贡献于能量密度，为何此类涡旋的引力响应在局部上与磁通含量无关？
• RQ3 在共维数为二的膜世界模型中，膜局域磁通能否在不违反引力约束的前提下实现紫外完备化？
• RQ4 在紧致化的额外维中，弦上与弦外的曲率如何依赖于张力与磁通等涡旋属性？
• RQ5 动能混合在实现体空间渗透磁通及稳定涡旋周围几何结构中起什么作用？

主要发现

• 暗涡旋的引力响应对局域磁通量大小不敏感；仅张力与磁通耦合起作用，与微观细节无关。
• 缺陷角与弦上曲率仅由张力 $ T_b $ 和磁通 $ \zeta_b $ 决定，与磁场强度无关。
• 膜局域磁通不直接产生引力，但以与磁场无关的方式修正张力。
• 在小翘曲极限下，度规呈现橄榄球状形式，其半径 $ r $ 与缺陷参数 $ \alpha $ 均依赖于 $ T_b $ 与 $ \zeta_b $。
• 翘曲因子在体空间中的变化量为 $ \Delta W \propto (T_+ - T_-) $，修正项按 $ \kappa^2 L_{\pm} $ 缩放，表明对张力差异敏感。
• 该有效理论通过提供紫外完备且光滑的解，解决了狄拉克δ函数处理中的悖论，使磁通与张力在引力中一致耦合。