The large D limit of planar diagrams

We show that in O(D) invariant matrix theories containing a large number D of complex or Hermitian matrices, one can define a D -> infinity 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.