Gradient flow exact renormalization group 1

Wilson’s exact renormalization group (ERG), which tells how a system changes under the scale transformation, provides a fundamental framework to define quantum field theory even beyond the perturbation theory. It has however been known that it is difficult to preserve a manifest gauge symmetry in ERG because of the usage of the momentum cutoff in ERG. Here, we propose a possible modification of ERG, the gradient flow exact renormalization (GFERG), which preserves a manifest gauge symmetry being based on a gauge-covariant diffusion equation. I explain the basic idea and properties of GFERG. If time permits, I want to present a possible application of GFERG to the consideration of the axial anomaly.