Exact solutions and residual regulator dependence in functional renormalisation group flows

TL;DR

This paper derives exact solutions to the functional renormalisation group equations for certain models at large N, revealing which physical quantities are regulator-independent and providing a new algorithm for operator basis construction.

Contribution

It presents the first exact solutions to FRG equations at large N without fixing the regulator, clarifying regulator dependence of physical quantities and introducing a systematic operator basis construction method.

Findings

Universal quantities like critical exponents are regulator-independent.

Values of coupling constants depend on the regulator choice.

Finite vacuum expectation values are qualitative features independent of regulator.

Abstract

We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for $2<d<4$, without specifying the form of the regulator. This allows to investigate which quantities are independent of the choice of regulator without being plagued by truncation artefacts. We find that only universal quantities, like critical exponents, and qualitative features, like the existence of a finite vacuum expectation value, are regulator-independent, whereas values of coupling constants are generically arbitrary. We also provide a general algorithm to construct a concrete operator basis for truncations in the derivative expansion and the Blaizot-M\'endez-Wschebor scheme.