Universality and the Renormalisation Group

TL;DR

This paper compares various functional renormalisation group equations, highlighting their similarities and differences, especially in stability and universality, using O(N) scalar theories as a case study.

Contribution

It demonstrates that Polchinski and ERG flows share universal content when properly optimized, despite differences in their derivative expansions.

Findings

Polchinski and ERG flows have identical universal content after optimization.

Stability and minimum sensitivity are crucial in comparing RG flows.

Extensions to higher order flows are discussed.

Abstract

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and differences are highlighted with special emphasis on stability properties. The main observations are worked out at the example of O(N) symmetric scalar field theories where the flows, universal critical exponents and scaling potentials are compared within a derivative expansion. To leading order, it is established that Polchinski flows and ERG flows - despite their inequivalent derivative expansions - have identical universal content, if the ERG flow is amended by an adequate optimisation. The results are also evaluated in the light of stability and minimum sensitivity considerations. Extensions to higher order and further implications are emphasized.