On level crossing in conformal field theories

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.