# 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.
Document type :
Preprints, Working Papers, ...

https://hal-cea.archives-ouvertes.fr/cea-01297362
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Submitted on : Monday, April 4, 2016 - 11:07:34 AM
Last modification on : Monday, December 13, 2021 - 9:16:04 AM

### Identifiers

• HAL Id : cea-01297362, version 1
• ARXIV : 1512.05362

### Citation

G. P. Korchemsky. On level crossing in conformal field theories. 2016. ⟨cea-01297362⟩

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