The large $D$ limit of planar diagrams

Abstract

We show that in O$(D)$ invariant matrix theories containing a large number $D$ of complex or Hermitian matrices, one can define a $D\to \infty$ 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.