Anomalous dimensions in hypercubic theories

Autor: Alexander Bednyakov, Johan Henriksson, Stefanos R. Kousvos
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Journal of High Energy Physics, Vol 2023, Iss 11, Pp 1-58 (2023)
Druh dokumentu: article
ISSN: 1029-8479
DOI: 10.1007/JHEP11(2023)051
Popis: Abstract We perform a comprehensive perturbative study of the operator spectrum in multi-scalar theories with hypercubic global symmetry. This includes working out symmetry representations and their corresponding tensor structures. These structures are then used to compute the anomalous dimensions of scalar operators with up to four fields and arbitrary representations to six-loop order. Moreover, we determine one-loop anomalous dimensions for a large number of low-lying operators in the spectrum which include more powers of the fundamental field and/or insertions of derivatives. As an aside we show how projectors used in the conformal bootstrap can be conveniently reused in computations of anomalous dimensions. The results of our study are of use to the conformal bootstrap. They also illuminate features of conformal perturbation theory and the large n expansion. Our results may be of interest for various crossover phenomena in statistical field theory. In total, we compute the scaling dimension of more than 300 operators, of which 16 are computed to six-loops. Our analysis is exhaustive with respect to group theory up to rank 4 for any number of flavours n, and also exhaustive with respect to which representations exist for n ⩽ 4.
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