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Peer-reviewedCC BY 4.0SciPost Physics

New instantons for matrix models

  • Marcos Mariño1
  • Ricardo Schiappa2,3,4,5
  • Maximilian Schwick2,3,4,5
5 affiliations
  1. 1University of Geneva
  2. 2Centro de Análise Matemática Geometria e Sistemas Dinâmicos
  3. 3Instituto Superior Técnico
  4. 4Isaac Newton Institute for Mathematical Sciences
  5. 5University of Lisbon
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Abstract

The complete, nonperturbative content of random matrix models is described by resurgent-transseries—general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models—but on the non-physical sheet of the spectral curve describing their large- N N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these “anti” eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painlevé I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.

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Cite

BibTeXRIS
BibTeX
@article{marino2026instantons,
  title = {{New instantons for matrix models}},
  author = {Marcos Mariño and Ricardo Schiappa and Maximilian Schwick},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.098},
  url = {https://doi.org/10.21468/scipostphys.21.4.098},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - New instantons for matrix models
AU  - Marcos Mariño
AU  - Ricardo Schiappa
AU  - Maximilian Schwick
PY  - 2026
DA  - 2026/10/21
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.098
UR  - https://doi.org/10.21468/scipostphys.21.4.098
AB  - The complete, nonperturbative content of random matrix models is described by resurgent-transseries—general solutions to their corresponding string-equations. These transseries include exponentially-suppressed multi-instanton amplitudes obtained by eigenvalue tunneling, but they also contain exponentially-enhanced and mixed instanton-like sectors with no known matrix model interpretation. This work shows how these sectors can be also described by eigenvalue tunneling in matrix models—but on the non-physical sheet of the spectral curve describing their large- N N limit. This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. How to calculate these “anti” eigenvalue-tunneling amplitudes is explained in detail and in various examples, such as the cubic and quartic matrix models, and their double-scaling limit to Painlevé I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.
SN  - 2542-4653
ER  -