Optimized renormalization group flows

TLDR

The study investigates optimizing exact renormalization group (ERG) flows. The authors compare specific optimized regulators for bosonic and fermionic fields with generic ERG flows, analyzing the results up to second order in the derivative expansion at both zero and finite temperature. They find that optimized flows at finite temperature factorize, separating thermal and quantum fluctuations, a similar factorization occurs at second order, and the optimized proper‑time renormalization group flow is provided to leading order.

Abstract

We study the optimization of exact renormalization group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimized by appropriate choices of the regularization. We consider specific optimized regulators for bosonic and fermionic fields and compare the optimized ERG flows with generic ones. This is done up to second order in the derivative expansion at both vanishing and nonvanishing temperature. We find that optimized flows at finite temperature factorize. This corresponds to the disentangling of thermal and quantum fluctuations. A similar factorization is found at second order in the derivative expansion. The corresponding optimized flow for a ``proper-time renormalization group'' is also provided to leading order in the derivative expansion.