Melonic limits of the quartic Yukawa model and general features of melonic CFTs

We study a set of large-$N$ tensor field theories with a rich structure of fixed points, encompassing both the melonic and prismatic CFTs observed previously in the conformal limits of other tensor theories and in the generalised Sachdev-Ye-Kitaev (SYK) model. The tensor fields interact via an $O(N)^3$-invariant generalisation of the quartic Yukawa model, $\phi^2\bar{\psi}\psi+\phi^6$. To understand the structure of IR/UV fixed points, we perform a partial four-loop perturbative analysis in $D=3-\epsilon$. We identify the flows between the melonic and prismatic fixed points in the bosonic and fermionic sectors, finding an apparent line of fixed points in both. We reproduce these fixed points non-perturbatively using the Schwinger-Dyson equations, and in addition identify the supersymmetric fixed points in general dimension. Selecting a particular fermionic fixed point, we study its conformal spectrum non-perturbatively, comparing it to the sextic prismatic model. In particular, we establish the dimensional windows in which this theory remains stable. We comment on the structure of large-$N$ melonic CFTs across various dimensions, noting a number of features which we expect to be common to any such theory.