New Instantons for Matrix Models

Marcos Marino; Ricardo Schiappa; Maximilian Schwick

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arXiv · 2210.13479

New Instantons for Matrix Models

Marcos Marino·Ricardo Schiappa·Maximilian Schwick

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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 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.

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hep-th cond-mat.stat-mech math-ph math.MP nlin.SI

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Marcos Marino, Ricardo Schiappa, Maximilian Schwick. 2022-10-24. New Instantons for Matrix Models. https://arxiv.org/abs/2210.13479

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