In this paper the fixed-point Wilson action for the critical $O(N)$ model in $D=4-ϵ$ dimensions is written down in the ϵ expansion to order ${ϵ}^2$. It is obtained by solving the fixed-point Polchinski Exact Renormalization Group equation (with anomalous dimension) in powers of ϵ. This is an example of a theory that has scale and conformal invariance despite having a finite UV cutoff. The energy-momentum tensor for this theory is also constructed (at zero momentum) to order ${ϵ}^2$. This is done by solving the Ward-Takahashi identity for the fixed point action. It is verified that the trace of the energy-momentum tensor is proportional to the violation of scale invariance as given by the exact RG, i.e., the β function. The vanishing of the trace at the fixed point ensures conformal invariance. Some examples of calculations of correlation functions are also given.

本文针对临界点的威尔逊定点动作 $Ø（ñ）$ 示范 $d=4-ϵ$尺寸已按顺序扩展ϵ${ϵ}^2$。它是通过求解在权力定点Polchinski精确重整化群方程（具有反常尺寸）得到ε。这是一个理论示例，尽管具有有限的UV截止值，但它具有比例和共形不变性。此理论的能量动量张量也按零动量构造${ϵ}^2$。这是通过解决定点动作的Ward-Takahashi身份来完成的。证实了能量动量张量的轨迹与由精确RG即β函数给出的尺度不变性的违反成比例。固定点处的迹线消失可确保保形不变。还给出了相关函数计算的一些示例。