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

TL;DR

This paper explores large-$N$ tensor field theories with melonic and prismatic fixed points, analyzing their structure, stability, and spectra across dimensions using perturbative and non-perturbative methods, revealing features common to melonic CFTs.

Contribution

It introduces a generalized quartic Yukawa tensor model with fixed points, studies their flows and spectra, and identifies supersymmetric solutions across dimensions, advancing understanding of melonic conformal field theories.

Findings

Identified flows between melonic and prismatic fixed points.

Reproduced fixed points non-perturbatively via Schwinger-Dyson equations.

Established stability windows for the theories across dimensions.

Abstract

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.