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New Instantons for Matrix Models
High Energy Physics - Theory · Submitted 24 Oct 2022 · Published version
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The complete, nonperturbative content of random matrix models is described by resurgent-transseries -- general solutions to their corresponding string-equations. | background 1.00 | 0.11 | 0.12 | asserted 1.00 |
| s1 | 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. | gap 0.68 | 0.13 | 0.07 | asserted 1.00 |
| s2 | 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. | contribution 0.61 | 0.91 | 0.74 | asserted 0.99 |
| s3 | This picture further explains the full resurgence of random matrices via analysis of all possible eigenvalue integration-contours. | interpretation 0.85 | 0.82 | 0.15 | asserted 0.95 |
| s4 | 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. | method 0.77 | 0.89 | 0.09 | asserted 1.00 |
| s5 | This further provides direct matrix-model derivations of their resurgent Stokes data, which were recently obtained by different techniques. | result 0.70 | 0.88 | 0.12 | asserted 1.00 |
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The paper
Original 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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References
How the literature uses it
17 arXiv papers cite this in 39 sentences
Papers citing it · 31 sentences without a confident label
Builds on it 1 paper
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The result of [ref] can be extended to negative instantons as follows [ref]
Large N instantons, BPS states, and the replica limit · The one-cut matrix model · 1.00
Uses its method or tool 2 papers
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It does not denote complex conjugation.] as: [equation] where we define the super-Vandermonde determinant [equation] and the $PV$ denotes a particular regularization prescription required to render the integral finite [ref] .
Complex eigenvalue instantons and the Fredholm determinant expansion in the Gross-Witten-Wadia model · Ghost-instanton contribution from tunneling anti-eigenvalues · 0.90
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It would be interesting to see explicitly how this happens in examples, deploying the non-perturbative techniques of e.g. [ref] .
Explicit large $N$ von Neumann algebras from matrix models · Conclusions and outlook · 0.93
Compares with it 1 paper
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This situation strongly resembles the one considered in [ref] where the anti-instantons in the matrix models are clearly identified.
Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph · Eigenvalue instantons and anti-instantons at finite N and dual gravity configurations · 0.97
Cites it as background 4 papers
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See [ref] for a detailed discussion of ghost instantons.
Giant graviton expansion from eigenvalue instantons · Introduction · 0.98
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The general trans-series solution to this equation was studied in [ref] and it involves both instantons and “anti-instantons," as well as mixed sectors (see [ref] for further studies of this type of trans-series solutions to non-linear ODEs, and [ref] for a recent matrix model interpretation).
On the resurgent structure of quantum periods · Multi-instanton solutions · 0.90
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These mixed sectors were first considered in a related context in [ref] , see [ref] for further developments.
Non-Perturbative Real Topological Strings · Multi-instantons · 0.85
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