A matrix CFT at multiple large charges

Abstract

We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show the existence of at least two distinct fixed points of the renormalization group (RG) flow. In particular, the one type of those fixed points manifests itself via tractable deviations in the large-charge expansion from the known predictions in the literature. We demonstrate most of the novel features using mainly the example of the $\text{SU}(4)$ matrix theory to compute the anomalous dimension of the lowest scalar operator with large global charge(s).