Physical-degree-of-freedom validity of conventional ERG ansätze

Determine whether conventional exact renormalization group ansätze that satisfy the nonlinear gauge Ward–Takahashi identity are genuinely describing the correct physical degrees of freedom.

Background

The paper contrasts the gradient flow exact renormalization group (GFERG) with conventional exact renormalization group formulations for gauge theories. In conventional ERG approaches, constructing an ansatz that satisfies the nonlinear gauge Ward–Takahashi identity is difficult. The authors state that, even when such an ansatz is constructed, it is unclear whether the resulting formulation actually captures the correct physical degrees of freedom. This uncertainty motivates the authors’ emphasis on GFERG, whose ansatz can satisfy the gauge Ward–Takahashi identity exactly and manifestly preserve gauge symmetry.