The Large D Limit of Planar Diagrams

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 $D\to \infty$ 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.

arXiv comment21 pages, 5 figures; v2: typos corrected, a few comments and references added; v3: a few references added, remarks on gauging and on the commutator squared interaction added. Published version