论文标题
$ O（N）$模型的Wilson Action
Wilson Action for the $O(N)$ Model
论文作者
论文摘要
在本文中，$ d = 4- \ eps $ dimensions中关键$ o（n）$模型的固定点作用写在$ \ eps $扩展中，以订购$ \ eps^2 $。它是通过求解$ \ eps $的powers polchinski精确重新归一化组方程（具有异常维度）来获得的。这是一个理论的一个例子，尽管有有限的紫外线截止，但具有规模和保形不变性。还构建了该理论的能量量张量（零动量），以订购$ \ eps^2 $。这是通过解决固定点作用的沃德 - 塔卡哈西身份来完成的。可以验证的是，能量量张量的痕迹与精确的RG（即$β$函数）给出的违反规模不变性成正比。固定点上的痕迹消失可确保保形不变性。还给出了一些相关函数计算的示例。
In this paper the fixed-point Wilson action for the critical $O(N)$ model in $D=4-\eps$ dimensions is written down in the $\eps$ expansion to order $\eps^2$. It is obtained by solving the fixed-point Polchinski Exact Renormalization Group equation (with anomalous dimension) in powers of $\eps$. 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 $\eps^2$. 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.
