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Register a new userSpectrum of anomalous dimensions in hypercubic theories
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Jahmall Matteo Bersini
Publication date
2019
fields
Physics
and research's language is
English
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We compute the spectrum of anomalous dimensions of non-derivative composite operators with an arbitrary number of fields $n$ in the $O(N)$ vector model with cubic anisotropy at the one-loop order in the $epsilon$-expansion. The complete closed-form expression for the anomalous dimensions of the operators which do not undergo mixing effects is derived and the structure of the general solution to the mixing problem is outlined. As examples, the full explicit solution for operators with up to $n=6$ fields is presented and a sample of the OPE coefficients is calculated. The main features of the spectrum are described, including an interesting pattern pointing to the deeper structure.
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We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given charge configuration and the associated operators for more involved symmetry groups such as the $U(N) times U(M)$. We show how, varying the charge configuration, it is possible to access anomalous dimensions of different operators transforming according to a variety of irreducible representations of the non-abelian symmetry group without the aid of diagrammatical computations. We illustrate our computational strategy by determining the anomalous dimensions of several composite operators to the next-to-leading order in the semiclassical expansion for the $U(N) times U(M)$ conformal field theory (CFT) in $4-epsilon$ dimensions. Thanks to the powerful interplay between semiclassical methods and group theory we can, for the first time, extract scaling dimensions for a wide range of operators.
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