Eur. Phys. J. C (2018) 78: 30
https://doi.org/10.1140/epjc/s10052-017-5505-2

Regular Article - Theoretical Physics

Functional perturbative RG and CFT data in the -expansion

¹ CP³-Origins, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark
² INFN-Sezione di Bologna, via Irnerio 46, 40126, Bologna, Italy
³ Dipartimento di Fisica e Astronomia, Friedrich-Schiller-Universität Jena, via Irnerio 46, 40126, Bologna, Italy
⁴ Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743, Jena, Germany

^* e-mail: vacca@bo.infn.it

Received: 26 October 2017
Accepted: 22 December 2017
Published online: 15 January 2018

Abstract

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group-based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the -expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models . Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.