New Instantons for Matrix Models

Fuente: arXiv
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Hauptverfasser: Marino, Marcos, Schiappa, Ricardo, Schwick, Maximilian
Format: Preprint
Veröffentlicht: 2022
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author Marino, Marcos
Schiappa, Ricardo
Schwick, Maximilian
author_facet Marino, Marcos
Schiappa, Ricardo
Schwick, Maximilian
contents 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 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 Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.
format Preprint
id arxiv_https___arxiv_org_abs_2210_13479
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle New Instantons for Matrix Models
Marino, Marcos
Schiappa, Ricardo
Schwick, Maximilian
High Energy Physics - Theory
Statistical Mechanics
Mathematical Physics
Exactly Solvable and Integrable Systems
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 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 Painleve I. This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques.
title New Instantons for Matrix Models
topic High Energy Physics - Theory
Statistical Mechanics
Mathematical Physics
Exactly Solvable and Integrable Systems
url https://arxiv.org/abs/2210.13479