论文标题
运行o $（n）$自由能和磁盘电容器的耦合和非扰动校正
Running coupling and non-perturbative corrections for O$(N)$ free energy and for disk capacitor
论文作者
论文摘要
我们重新考虑了线性TBA方程的完整解决方案，该方程描述了Wiener-HOPF方法中$ O（n）$ nlinear Sigma模型中有限密度状态的能量密度。我们保留所有扰动和非扰动的贡献，并引入一个运行的耦合，其中所有渐近系列出现在问题中的渐近系列都可以表示为没有日志的纯电源序列。我们在$ o（3）$案件中提出了第一个非扰动贡献，并表明（大概是由于instanton校正）复兴理论在此示例中失败了。利用$ O（3）$问题与同轴磁盘电容器问题的关系，我们为后者解决了领先的非扰动术语，并表明（至少在此顺序）复活理论，尤其是中间的重新点燃处方，给出了正确的答案。我们通过将Wiener-HOPF结果与原始积分方程的高精度数值解相提并论来证明这一点。
We reconsider the complete solution of the linear TBA equation describing the energy density of finite density states in the $O(N)$ nonlinear sigma models by the Wiener-Hopf method. We keep all perturbative and non-perturbative contributions and introduce a running coupling in terms of which all asymptotic series appearing in the problem can be represented as pure power series without logs. We work out the first non-perturbative contribution in the $O(3)$ case and show that (presumably because of the instanton corrections) resurgence theory fails in this example. Using the relation of the $O(3)$ problem to the coaxial disks capacitor problem we work out the leading non-perturbative terms for the latter and show that (at least to this order) resurgence theory, in particular the median resummation prescription, gives the correct answer. We demonstrate this by comparing the Wiener-Hopf results to the high precision numerical solution of the original integral equation.
