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

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...

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Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Balog, Ivan, De Polsi, Gonzalo, Tissier, Matthieu, Wschebor, Nicolás
Format: Article
Language:English
Subjects:
Exponents
Group theory
Invariance
Ising model
Regularization
Regulators
Three dimensional models
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.02521