AI 中文总结
本文针对三维U(1)规范理论原连续极限的病态问题，通过扩展Wilson作用量引入参数μ，找到物理常数线，使胶球质量与弦张力平方根的比值恒定，有望得到表现良好的连续极限。
AI 中文摘要
在三维紧致U(1)格点规范理论中，色禁闭可通过磁单极子的动力学进行解析理解。然而，其连续极限存在病态问题，因为当趋近连续极限时，胶球质量与弦张力平方根的比值会消失。我们研究了Wilson作用量的一种简单扩展，其中格点磁单极子的总数与一个额外参数μ耦合。通过同时调整β和μ，我们确定了一条物理常数线，沿该线最轻胶球质量与弦张力平方根的比值保持恒定。我们进一步表明，在数值不确定度范围内，本研究中考虑的其他低能胶球质量也满足相同的标度关系。沿该轨迹，以格点单位衡量的弦张力随β增大而减小，这表明修改后的格点作用量可能为三维紧致U(1)规范理论提供一种正则化方案，且该理论具有物理上表现良好的连续极限。
英文摘要
In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter $μ$. By tuning $β$ and $μ$ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing $β$, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.
Comments18 pages, 6 pdf figures
