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 phi _{i_1} dots phi _{i_m}. For all such models we analyze to the leading order of the epsilon -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 as well as for all the even models. We ultimately specialize to S_q 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 frac{10}{3}, which can thus be nontrivial CFTs in three dimensions.
Highlights
Their upper critical dimension, which is defined as the dimensionality above which a quantum field theories (QFTs) exhibits Gaussian exponents, these QFTs are generally interacting
We specialize to Sq symmetric models, which are related to the q-state Potts universality class, and focus on three realizations appearing below the upper critical dimensions
We have employed a general method based on the use of conformal symmetry and Schwinger–Dyson equations to investigate multicritical multi-field scalar QFTs, characterized by a critical potential of order m
Summary
Their upper critical dimension, which is defined as the dimensionality above which a QFT exhibits Gaussian exponents, these QFTs are generally interacting. In this work we concentrate on a CFT-based method which determines the conformal data of a theory in the expansion by requiring consistency between the Schwinger– Dyson equation (SDE), related to a general action at criticality, and conformal symmetry in the Gaussian limit → 0 [46]. The idea of the SDE+CFT approach is to move below the upper critical dimension dc, above which the theory is Gaussian, and interpolate the nontrivial correlators shown above with those of the trivial Gaussian theory as a function of the critical coupling The consistency of this interpolation determines the leading order corrections in of some conformal data when one exploits further relations between operators that are primary only in the Gaussian limit. The second includes three parts reporting in order: the reduction relations for Sq symmetric tensors, some computational details for the quintic model, and few useful RG results [64] needed for the quintic model
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
