On level crossing in conformal field theories

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.

20 pages, 4 figures; v2: minor corrections, references added

References in corpus (2)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Comments on operators with large spin

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