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Annales de l’Institut Henri Poincaré D

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Volume 6, Issue 3, 2019, pp. 427–448
DOI: 10.4171/AIHPD/76

Published online: 2019-09-04

The large $D$ limit of planar diagrams

Frank Ferrari[1]

(1) Université Libre de Bruxelles and Intern. Solvay Institutes, Bruxelles, Belgium and Inst. for Basic Sciences, Daejeon, S

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.

Keywords: Feynman graphs, large $N$, large $D$, planar diagrams, matrix models, tensor models, holography, black holes

Ferrari Frank: The large $D$ limit of planar diagrams. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 6 (2019), 427-448. doi: 10.4171/AIHPD/76