Conformal invariance in the nonperturbative renormalization group: a rationale for choosing the regulator

Ivan Balog, Gonzalo De Polsi, Matthieu Tissier, Nicolás Wschebor

Published 2020-04-06Version 1

Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters, associated with the regularization of the theory or with the resummation procedure. In practical implementations of Wilson's renormalization group, the values of the critical exponents artificially depend on a regulating function, which obscures the determination of these physical quantities. In this article, we propose to choose this regulating function by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the so-called derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the Ward identity associated with this symmetry is not exactly satisfied. The regulators which minimize the violation of this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap.