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arXiv 1009.2104hep-phastro-ph.COhep-th
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Nielsen-Olesen涡旋的推广：修正的Abelian-Higgs模型中的非圆柱弦

A Generalisation of the Nielsen-Olesen Vortex: Non-cylindrical strings in a modified Abelian-Higgs model

Matthew Lake, John Ward

备注：
35 pages, 2 figures, published version
发表信息：
JHEP 1104:048,2011
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摘要：

我们通过引入标量场和矢量场的空间依赖耦合来修改标准阿贝尔-希格斯模型。我们调查静态的，非圆柱对称的解决方案所产生的场方程，并提出了一个箍缩的解决方案，沿字符串，标记为$\pm |n|$退化真空之间的插值。这种结构对应于一个涡旋，它在作为反涡旋重新出现之前收缩到普朗克尺度，导致形成一个珠对，其中一个珠在交叉点的两侧。该解是拓扑稳定的。一个关键的假设是，相位和绕组数等量，以及依赖于它们的量，如磁通量，在普朗克尺度下变得不确定，因此相反绕组的区域可以通过普朗克尺寸的中性弦连接起来。讨论了这个解与IIB型弦论中弦的额外维缠绕之间的相似性，并提出了场论与弦论参数之间的对应关系。场耦合的空间依赖性被发现有一个自然的解释，在双弦图片和结果的缠绕半径的变化，从而产生一个变化的（有效的）字符串耦合。一个有趣的结果是希格斯质量的估计（在临界耦合）的参数定义的克列巴诺夫-斯特拉斯勒几何，这在原则上，可能会受到宇宙学观测。

英文摘要：

We modify the standard Abelian-Higgs model by introducing spatially-dependent couplings for the scalar and vector fields. We investigate static, non-cylindrically symmetric solutions of the resulting field equations and propose a pinch solution which interpolates between degenerate vacua along the string, labelled by $\pm |n|$. This configuration corresponds to a vortex which shrinks to Planck scale before re-emerging as an anti-vortex, resulting in the formation of a bead pair with one bead at either side of the intersection. The solution is then topologically stable. A key assumption is that quantities such as phase and winding number, along with those which depend on them like the magnetic flux, become undefined at the Planck scale so that regions of opposite winding may be joined via a Planck-sized segment of neutral string. Similarities between this solution and the extra-dimensional windings of strings in type IIB string theory are discussed and a correspondence between field theory and string theory parameters is suggested. The spatial-dependence of the field couplings is found to have a natural interpretation in the dual string picture and results from the variation of the winding radius, giving rise to a varying (effective) string coupling. An interesting result is an estimate of the Higgs mass (at critical coupling) in terms of the parameters which define the Klebanov-Strassler geometry and which, in principle, may be constrained by cosmological observations.

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