More on the New Large $D$ Limit of Matrix Models

TL;DR

This paper extends the large D limit analysis of matrix models to include multi-trace interactions and various symmetries, revealing conditions for consistency and exploring implications for bosonic and supersymmetric models.

Contribution

It introduces a generalized large D limit framework for matrix models with multi-trace interactions and different symmetries, clarifying consistency conditions and properties of bosonic and supersymmetric models.

Findings

Large D limit is consistent for planar diagrams with certain symmetry conditions.

Higher genus diagrams require tracelessness for consistency.

Standard IR behavior arguments do not apply to bosonic models.

Abstract

In this paper, we extend the recent analysis of the new large $D$ limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases of complex and Hermitian matrices, with $\text{U}(N)^{2}\times\text{O}(D)$ and $\text{U}(N)\times\text{O}(D)$ symmetries respectively. In the latter case, the new large $D$ limit is consistent for planar diagrams; at higher genera, it crucially requires the tracelessness condition. For similar reasons, the large $N$ limit of tensor models with reduced symmetries is typically inconsistent already at leading order without the tracelessness condition. We also further discuss some interesting properties of purely bosonic models pointed out recently and explain that the standard argument predicting a non-trivial IR behaviour in fermionic models \`a la SYK does not work for bosonic models. Finally, we explain that the new large $D$ scaling is consistent with linearly realized supersymmetry.