# Leading order CFT analysis of multi-scalar theories in d>2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d>2$\end{document}

Codello, A. (Aff1, Department of Physics, Southern University of Science and Technology, 518055, Shenzhen, China) ; Safari, M. (Aff2, grid.470193.8, INFN - Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy) (Aff3, 0000 0004 1757 1758, grid.6292.f, Dipartimento di Fisica e Astronomia, Via Irnerio 46, 40126, Bologna, Italy) ; Vacca, G. P.  (Aff2, grid.470193.8, INFN - Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy) ; Zanusso, O.  (Aff2, grid.470193.8, INFN - Sezione di Bologna, Via Irnerio 46, 40126, Bologna, Italy) (Aff4, 0000 0001 1939 2794, grid.9613.d, Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743, Jena, Germany)

12 April 2019

Abstract: We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger–Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define to admit a Landau–Ginzburg description that includes the most general critical interactions built from monomials of the form ϕi1⋯ϕim \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\phi _{i_1} \dots \phi _{i_m}$\end{document} . For all such models we analyze to the leading order of the ϵ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\epsilon$\end{document} -expansion the anomalous dimensions of the fields and those of the composite quadratic operators. For models with even m we extend the analysis to an infinite tower of composite operators of arbitrary order. The results are supplemented by the computation of some families of structure constants. We also find the equations which constrain the nontrivial critical theories at leading order and show that they coincide with the ones obtained with functional perturbative RG methods. This is done for the case m=3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$m=3$\end{document} as well as for all the even models. We ultimately specialize to Sq \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$S_q$\end{document} symmetric models, which are related to the q -state Potts universality class, and focus on three realizations appearing below the upper critical dimensions 6, 4 and 103 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\frac{10}{3}$\end{document} , which can thus be nontrivial CFTs in three dimensions.

Published in: EPJC 79 (2019) 331 DOI: 10.1140/epjc/s10052-019-6817-1