再论Wilson-Fisher不动点的伸缩算子
Revisiting the dilatation operator of the Wilson-Fisher fixed point
摘要：
我们根据共形场论的最新结果重新讨论了由Kehrein，Pismak和Wegner得到的Wilson-Fisher不动点的阶$\varepsilon$伸缩算子.我们的方法是代数的，只基于对称性原则。我们的分析的出发点是，第一个修正的伸缩算子是一个共形不变量，这意味着它的形式是固定到一个无限的系数集与高自旋电流的标度尺寸。这些系数可以固定使用众所周知的微扰结果，然而，他们最近重新获得使用CFT参数，而不依赖于微扰理论。我们的分析，然后意味着所有的顺序$\varepsilon$标度尺寸的威尔逊-费舍尔不动点可以固定的对称性。
英文摘要：
We revisit the order $\varepsilon$ dilatation operator of the Wilson-Fisher fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results in conformal field theory. Our approach is algebraic and based only on symmetry principles. The starting point of our analysis is that the first correction to the dilatation operator is a conformal invariant, which implies that its form is fixed up to an infinite set of coefficients associated with the scaling dimensions of higher-spin currents. These coefficients can be fixed using well-known perturbative results, however, they were recently re-obtained using CFT arguments without relying on perturbation theory. Our analysis then implies that all order-$\varepsilon$ scaling dimensions of the Wilson-Fisher fixed point can be fixed by symmetry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
