论文标题
重新审视高温下的半古典近似
The semi-classical approximation at high temperature revisited
论文作者
论文摘要
我们在四个维度的非亚洲仪表理论中在有限温度下的激体温度下的尺寸分布进行了半古典计算。首先在Gross，Pisarski和Yaffe的开创性工作中计算相关的功能决定因素，结果用于包括轴在内的多种应用。在这项工作中，我们表明，数值评估和半分析表达式的不确定性比声称的两个数量级。结果，需要重新评估从尺寸分布计算的各种数量，例如，任意高温下拓扑敏感性的相对误差约为QCD 5％，对于$ SU（3）$ yang-mills理论约为10％。随着排名较高的组组，这种差异甚至更高。我们还为尺寸分布提供了一个简单的半分析公式，并具有绝对错误$ 2 \ cdot10^{ - 4} $。此外，我们还纠正了MSBAR方案中激数尺寸分布的全部常数，如果存在非平凡的费用含量，则在文献中被错误地使用。
We revisit the semi-classical calculation of the size distribution of instantons at finite temperature in non-abelian gauge theories in four dimensions. The relevant functional determinants were first calculated in the seminal work of Gross, Pisarski and Yaffe and the results were used for a wide variety of applications including axions most recently. In this work we show that the uncertainty on the numerical evaluations and semi-analytical expressions are two orders of magnitude larger than claimed. As a result various quantities computed from the size distribution need to be reevaluated, for instance the resulting relative error on the topological susceptibility at arbitrarily high temperatures is about 5% for QCD and about 10% for $SU(3)$ Yang-Mills theory. With higher rank gauge groups this discrepancy is even higher. We also provide a simple semi-analytical formula for the size distribution with absolute error $2\cdot10^{-4}$. In addition we also correct the over-all constant of the instanton size distribution in the MSbar scheme which was widely used incorrectly in the literature if non-trivial fermion content is present.
