Predictive power of renormalisation group flows: a comparison

TL;DR

This paper compares the predictive capabilities of the proper-time renormalisation group with the exact renormalisation group, analyzing their differences and implications through theoretical mapping and critical exponent calculations.

Contribution

It establishes an explicit leading-order map from the exact to the proper-time renormalisation group and discusses the limitations of the proper-time approach's predictiveness.

Findings

Proper-time RG is not exact and has limited predictive power.

An explicit leading-order map from the exact to proper-time RG is derived.

Critical exponents computed for O(N) theories show differences between the formalisms.

Abstract

We study a proper-time renormalisation group, which is based on an operator cut-off regularisation of the one-loop effective action. The predictive power of this approach is constrained because the flow is not an exact one. We compare it to the Exact Renormalisation Group, which is based on a momentum regulator in the Wilsonian sense. In contrast to the former, the latter provides an exact flow. To leading order in a derivative expansion, an explicit map from the exact to the proper-time renormalisation group is established. The opposite map does not exist in general. We discuss various implications of these findings, in particular in view of the predictive power of the proper-time renormalisation group. As an application, we compute critical exponents for O(N)-symmetric scalar theories at the Wilson-Fisher fixed point in 3d from both formalisms.