On level crossing in conformal field theories

TL;DR

This paper investigates the universal behavior of operator scaling dimensions and OPE coefficients near level crossing points in conformal field theories, supported by examples from supersymmetric Yang-Mills, 3D CFTs, and QCD.

Contribution

It introduces a universal scaling framework for operator dimensions and OPE coefficients near crossing points in unitary conformal field theories.

Findings

Universal scaling relations match known examples

Operator dimensions exhibit predictable behavior near crossings

OPE coefficients follow similar universal patterns

Abstract

We study the properties of operators in a unitary conformal field theory whose scaling dimensions approach each other for some values of the parameters and satisfy von Neumann-Wigner non-crossing rule. We argue that the scaling dimensions of such operators and their OPE coefficients have a universal scaling behavior in the vicinity of the crossing point. We demonstrate that the obtained relations are in a good agreement with the known examples of the level-crossing phenomenon in maximally supersymmetric $\mathcal N=4$ Yang-Mills theory, three-dimensional conformal field theories and QCD.