The gradient flow exact renormalization group (GFERG) is an exact renormalization group motivated by the Yang--Mills gradient flow and its salient feature is a manifest gauge invariance. We generalize this GFERG, originally formulated for the pure Yang--Mills theory, to vector-like gauge theories containing fermion fields, keeping the manifest gauge invariance. For the chiral symmetry we have two options: one possible formulation preserves the conventional form of the chiral symmetry and the other simpler formulation realizes the chiral symmetry in a modified form à la Ginsparg--Wilson. We work out a gauge-invariant local Wilson action in quantum electrodynamics to the lowest nontrivial order of perturbation theory. This Wilson action reproduces the correct axial anomaly in $D=2$.

中文翻译：

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梯度流精确重整化组：包含费米子场

梯度流精确重整化群（GFERG）是由Yang-Mills梯度流推动的精确重整化群，其显着特征是明显的规范不变性。我们将这个最初为纯杨-米尔斯理论制定的 GFERG 推广到包含费米子场的类矢量规范理论，保持明显的规范不变性。对于手性对称，我们有两种选择：一种可能的公式保留手性对称的传统形式，另一种更简单的公式以修改形式实现手性对称，如 Ginsparg-Wilson。我们将量子电动力学中的规范不变局部威尔逊作用计算到微扰理论的最低非平凡阶。这个 Wilson 动作在 $D=2$ 中重现了正确的轴向异常。