The Large D Limit of Planar Diagrams

TL;DR

This paper demonstrates that in large D limit of O(D) invariant matrix theories, the sum over planar diagrams simplifies to melon diagrams, enabling analysis of models related to black holes.

Contribution

It introduces a large D limit in matrix theories where planar diagrams reduce to melon diagrams, extending recent results from SYK and tensor models.

Findings

Planar diagram sum truncates to melon diagrams in large D limit

Results applicable to matrix models of black holes

Generalizes SYK and tensor model findings

Abstract

We show that in $\text{O}(D)$ invariant matrix theories containing a large number $D$ of complex or Hermitian matrices, one can define a $D\rightarrow\infty$ limit for which the sum over planar diagrams truncates to a tractable, yet non-trivial, sum over melon diagrams. In particular, results obtained recently in SYK and tensor models can be generalized to traditional, string-inspired matrix quantum mechanical models of black holes.