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 multi-critical models phi ^{2n}. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.
Highlights
The standard perturbative renormalization group (RG) and the -expansion have been, since the pioneering work of Wilson and Kogut [1], the main analytical tools for the analysis of critical phenomena and, more generally, for the study of universality classes with methods of quantum field theory (QFT)
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 approach of this work employs dimensional regularization in the MS scheme at the functional level and gives access to a specific set of “massless” OPE coefficients, which are related to terms in the beta functions that are universal at the upper critical dimensions of the models under investigation
Summary
The standard perturbative renormalization group (RG) and the -expansion have been, since the pioneering work of Wilson and Kogut [1], the main analytical tools for the analysis of critical phenomena and, more generally, for the study of universality classes with methods of quantum field theory (QFT). A CFT can be fully characterized by providing the socalled CFT data, which includes the scaling dimensions i of a set of operators known as primaries, and the structure constants Ci jk of their three point functions [3,4,5]. From the point of view of CFT, the scaling dimensions determine some of the most important properties of the scaling operators at criticality, and can be related to the critical exponents θi of an underlying second-order phase transition, while the structure constants provide further non-trivial information on the form of the correlators of the theory. It is natural to wonder to which extent the RG can help the determination of the remaining CFT data: the structure constants Ci jk, which have received far less attention in the RG literature
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