N味阿贝尔希格斯模型中的全局不动点势
Global Fixed Point Potentials in the Abelian Higgs Model with $N$ flavors
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中文总结 AI 辅助
本文利用函数重整化群研究d维N味阿贝尔希格斯模型的带电不动点，发现ε→1时ε展开失效，临界味数与微扰结果差异显著，d=3时或存在多临界点不动点，还探讨了相关规范问题与光子质量可能性。
中文摘要 AI 辅助
本文利用函数重整化群，研究d维N味阿贝尔希格斯模型中带电不动点的存在性。我们数值求解了标度依赖电荷与标量场非微扰有效势的耦合不动点方程。结果表明，在具有O(N)对称性的理论中取得成功的ε=4-d展开，在取ε→1极限时无法给出可靠结果。通过确定全局不动点势，我们发现带电不动点出现时的临界味数与微扰处理相比发生了显著改变。在d=3时，还发现了更丰富的不动点结构迹象，推测存在多临界点不动点。讨论内容包括规范固定的微妙性及对应的修正沃德-高桥恒等式，其中涉及红外不动点处存在非零无量纲光子质量的可能性。
英文摘要
Existence of charged fixed points in the Abelian Higgs model with $N$ flavors in $d$ dimensions is studied using the functional renormalization group. We numerically solve the coupled fixed point equations for the scale dependent charge and the non-perturbative effective potential for the scalar field. We show that the $ε=4-d$ expansion, famously successful in theories with $O(N)$ symmetry, fails to produce reliable results when taking the $ε\rightarrow 1$ limit. By determining global fixed point potentials, it is shown that the critical flavor number at which charged fixed points appear, modifies significantly compared to the perturbative treatment. In $d=3$, signs of a richer fixed point structure with presumably multicritical fixed points are also found. Discussions include subtleties of the gauge fixing and the corresponding modified Ward-Takahashi identities, including the possibility of a nonzero dimensionless photon mass at the infrared fixed point.
发表机构
- Institute of Physics and Astronomy, Eötvös University（厄特沃什大学物理与天文学研究所）
- Physics Department, Brookhaven National Laboratory（布鲁克海文国家实验室物理系）
- RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理研跨学科理论与数学科学中心（iTHEMS））
- Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能研究开发机构先进科学研究中心）
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