Multicritical Yukawa theories: a CFT analysis at leading order

Multicritical Yukawa unitary theories are considered here with the goal of studying the universal properties of systems with interacting fermionic and scalar degrees of freedom close to criticality. This work presents a detailed study of several key physical quantities, which are part of the defining CFT data for models with scalar self-interacting potentials ϕm and Yukawa interactions y ϕn−1 ¯ψψ. The scalar potential is taken even, i.e., m = 2n, which implies that the theory is unitary. Using a perturbative approach that combines the Schwinger-Dyson equations with the constraints imposed by conformal symmetry on correlation functions, the anomalous dimensions of fundamental and composite operators with spin 0 and 1/2, families of structure constants and the leading order expression of several correlation functions - which vanish in the Gaussian theory - are computed. These results provide the first systematic evaluation of such quantities at leading order below the upper critical dimension dm = 2m / m−2 and illustrate the nontrivial effects of Yukawa interactions in multicritical theories.