Generalized Wilson-Fisher critical points from the conformal OPE

TL;DR

This paper develops a method to compute anomalous dimensions of scalar operators in generalized free conformal field theories using conformal blocks and null states, applicable across dimensions and verified against existing methods.

Contribution

It introduces a novel approach leveraging conformal block singularities to derive anomalous dimensions without relying on equations of motion.

Findings

Derived anomalous dimensions at first order in epsilon-expansion.

Results agree with existing computational methods where applicable.

Applicable to arbitrary dimensions and a broad class of operators.

Abstract

We study possible smooth deformations of Generalized Free Conformal Field Theories in arbitrary dimensions by exploiting the singularity structure of the conformal blocks dictated by the null states. We derive in this way, at the first non trivial order in the $\epsilon$-expansion, the anomalous dimensions of an infinite class of scalar local operators, without using the equations of motion. In the cases where other computational methods apply, the results agree.