Functional perturbative RG and CFT data in the $\epsilon$-expansion

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 $\epsilon$-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 multicritical models $\phi^{2n}$. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.