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

Abstract

Field-theoretical calculations performed in an approximation scheme often present a spurious dependence of physical quantities on some unphysical parameters associated with the details of the calculation setup (such as, the renormalization scheme or, in perturbation theory, the resummation procedure). In the present article, we propose to reduce this dependence by invoking conformal invariance. Using as a benchmark the three-dimensional Ising model, we show that, within the derivative expansion at order 4, performed in the nonperturbative renormalization group formalism, the identity associated with this symmetry is not exactly satisfied. The calculations which best satisfy this identity are shown to yield critical exponents which coincide to a high accuracy with those obtained by the conformal bootstrap.

arXiv comment5 pages, 2 figures, Supplemental Material: 1 Mathematica notebook file (in source file)

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• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
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• ${\mathbb{Z}}_4$-symmetric perturbations to the XY model from functional renormalization
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