Geodesic
The large D limit of planar diagrams
Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 427-448.

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

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DOI : 10.4171/aihpd/76
Classification : 81-XX, 05-XX, 41-XX, 83-XX
Keywords: Feynman graphs, large $N$, large $D$, planar diagrams, matrix models, tensor models, holography, black holes 
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     title = {The large $D$ limit of planar diagrams},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {427--448},
     volume = {6},
     number = {3},
     year = {2019},
     doi = {10.4171/aihpd/76},
     mrnumber = {4002672},
     zbl = {1431.83092},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpd/76/}
}
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Ferrari, Frank. The large $D$ limit of planar diagrams. Annales de l’Institut Henri Poincaré D, Tome 6 (2019) no. 3, pp. 427-448. doi : 10.4171/aihpd/76. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/76/

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