Untangling scaling dimensions of fixed charge operators in Higgs theories

Oleg Antipin, Jahmall Bersini, Francesco Sannino, Zhi Wei Wang*, Chen Zhang

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Abstract

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)×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)×U(M) conformal field theory (CFT) in 4-ϵ 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.

OriginalsprogEngelsk
Artikelnummer125024
TidsskriftPhysical Review D
Vol/bind103
Udgave nummer12
Antal sider32
ISSN2470-0010
DOI
StatusUdgivet - 15. jun. 2021

Bibliografisk note

Funding Information:
The work of O.A. and J.B. is partially supported by the Croatian Science Foundation Project No. 4418 as well as European Union through the European Regional Development Fund'the Competitiveness and Cohesion Operational Programme (KK.01.1.1.06). F.S. and Z.W. acknowledge the partial support by Danish National Research Foundation Grant No. DNRF:90. We thank Johan Henriksson for his very helpful comments. For the group theoretical analyses, we made use of the Mathematica package LieART [80,81].

Funding Information:
The work of O. A. and J. B. is partially supported by the Croatian Science Foundation Project No. 4418 as well as European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme (KK.01.1.1.06). F. S. and Z. W. acknowledge the partial support by Danish National Research Foundation Grant No. DNRF:90. We thank Johan Henriksson for his very helpful comments. For the group theoretical analyses, we made use of the Mathematica package LieART .

Publisher Copyright:
© 2021 authors.

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