A matrix CFT at multiple large charges

TL;DR

This paper explores three-dimensional SU(N) matrix models with multiple large charges, revealing new fixed points and deviations in the large-charge expansion, exemplified through SU(4) to compute anomalous dimensions.

Contribution

It identifies at least two distinct RG fixed points in matrix models with multiple large charges, including novel deviations in the large-charge expansion from previous predictions.

Findings

Existence of multiple RG fixed points in SU(N) matrix models.

Novel deviations in large-charge expansion predictions.

Explicit computation of anomalous dimensions in SU(4) matrix theory.

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).