Gauge invariant non-perturbative Wilson action in quantum electrodynamics

By employing the gradient flow exact renormalization group (GFERG), we study the renormalization group (RG) flow of a manifestly gauge or BRST invariant non-perturbative ansatz of the 1PI Wilson action in quantum electrodynamics. The gauge invariance of the Wilson action is exactly preserved under the RG flow. We explicitly solve the GFERG equation in the leading and partially next-to-leading orders of the large Nf approximation, where Nf is the number of flavors. We obtain gauge invariant critical exponents and the gauge invariant 1PI Wilson action at an infrared (IR) fixed point for D < 4, where D is the spacetime dimension.