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The Large D Limit of Planar Diagrams

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arxiv 1701.01171 v3 pith:TAUC7ZJG submitted 2017-01-04 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords diagramslargelimitmatrixmodelsplanarblackcomplex
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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 $D\rightarrow\infty$ 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.

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  1. Critical dimensions and small cycle dominance from all-orders asymptotics of $d$-matrix theory

    hep-th 2026-03 conditional novelty 7.0 of 10

    The weighted partition numbers of d-matrix theory admit an all-orders asymptotic expansion that switches from divergent to convergent at d=13 (bosonic) or 7 (fermionic).

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