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Large N instantons from topological strings

by Marcos Mariño, Ramon Miravitllas

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Submission summary

Authors (as registered SciPost users): Marcos Mariño · Ramon Miravitllas
Submission information
Preprint Link:  (pdf)
Date accepted: 2024-05-27
Date submitted: 2024-05-20 09:35
Submitted by: Miravitllas, Ramon
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


The $1/N$ expansion of matrix models is asymptotic, and it requires non-perturbative corrections due to large $N$ instantons. Explicit expressions for large $N$ instanton amplitudes are known in the case of Hermitian matrix models with one cut, but not in the multi-cut case. We show that the recent exact results on topological string instanton amplitudes provide the non-perturbative contributions of large $N$ instantons in generic multi-cut, Hermitian matrix models. We present a detailed test in the case of the cubic matrix model by considering the asymptotics of its $1/N$ expansion, which we obtain at relatively high genus for a generic two-cut background. These results can be extended to certain non-conventional matrix models which admit a topological string theory description. As an application, we determine the large $N$ instanton corrections for the free energy of ABJM theory on the three-sphere, which correspond to D-brane instanton corrections in superstring theory. We also illustrate the applications of topological string instantons in a more mathematical setting by considering orbifold Gromov-Witten invariants. By focusing on the example of $\mathbb{C}^3/\mathbb{Z}_3$, we show that they grow doubly-factorially with the genus and we obtain and test explicit asymptotic formulae for them.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

List of changes

Added comments about the Fermi gas

Published as SciPost Phys. 16, 155 (2024)

Reports on this Submission

Anonymous Report 1 on 2024-5-20 (Invited Report)


The authors added a clarification about the issue raised in the previous
report. After the clarification, I recommend the paper for publication.


Publish (surpasses expectations and criteria for this Journal; among top 10%)

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