被巨涡旋俘获的费米子的零模
Zero Modes of Fermions Trapped by Giant Vortices
AI总结：
本文研究了 abelian Higgs 和 Chern-Simons Higgs 模型中被巨涡旋束缚的费米子零能解，通过逆幂展开得到了指标定理要求的渐近解析解，并揭示了两模型中零模分布的普适性与核心边界局域特性。
摘要：
本文研究了在 abelian Higgs 和 Chern-Simons Higgs 模型中，束缚于大绕数 $n$ 的巨涡旋上的费米子所满足的 Dirac 方程的零能解。详细讨论了拓扑超导体中 Majorana 态的 Jackiw-Rossi 理论。通过按 $n$ 的逆幂展开，我们得到了指标定理所要求的渐近所有 $n$ 个解的解析结果。在 abelian Higgs 模型中，零模填满涡旋核心，并展现出独立于规范场和标量场相互作用细节的普适结构，这特别决定了大 $n$ 超导宇宙弦的一般性质。相反，对于 Chern-Simons Higgs 涡旋，零模局域在核心边界上，并且在自对偶背景下针对超对称耦合获得了显式解。
英文摘要：
Zero-energy solutions of the Dirac equation for the fermions bound to giant vortices of large winding number $n$ are studied in the abelian Higgs and Chern-Simons Higgs models. The case of Jackiw-Rossi theory of the Majorana states in topological superconductors is discussed in detail. By expanding in inverse powers of $n$ we find an analytic result for asymptotically all $n$ solutions required by the index theorem. In the abelian Higgs model the zero modes fill the vortex core and reveal a universal structure independent of fine details of the gauge and scalar field interactions which, in particular, determines the general properties of the large-$n$ superconducting cosmic strings. On the contrary, for the Chern-Simons Higgs vortices the zero modes are localized on the core boundary and the explicit solution is obtained for the supersymmetric couplings in a self-dual background.
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