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Modular-Invariant Random Matrix Theory and AdS_{3} Wormholes
Jan Boruch1, Gabriele Di Ubaldo2, Felix M Haehl3
1University of California, Leinweber Institute for Theoretical Physics and Department of Physics, Berkeley, California 94720, USA.
Physical Review Letters
|October 5, 2025
Summary
We introduce a new definition for Random Matrix Theory in 2D (RMT2), compatible with conformal field theory symmetries. This framework generalizes spectral correlations and has applications in AdS3 gravity, particularly for wormhole amplitudes.
Area of Science:
- Mathematical Physics
- Quantum Field Theory
- String Theory
Background:
- Random Matrix Theory (RMT) is crucial in quantum mechanics and statistical physics.
- Two-dimensional conformal field theories (CFTs) possess unique symmetries.
- Existing RMT lacks direct compatibility with CFT symmetries.
Purpose of the Study:
- To define a nonperturbative Random Matrix Theory in 2D (RMT2) compatible with CFT symmetries.
- To establish a method for lifting RMT spectral correlations to RMT2.
- To explore applications of RMT2 in quantum gravity, specifically AdS3 gravity.
Main Methods:
- Developed a nonperturbative definition of RMT2.
- Utilized Mellin space representation of RMT.
- Employed SL(2,Z) spectral decomposition for lifting RMT to 2D.
- Calculated RMT2 lift of GUE Airy model correlations.
Main Results:
- A general prescription for modular-invariant lift of RMT spectral correlations to RMT2.
- RMT2 correlators reduce to original RMT correlators in a near-extremal limit.
- Demonstrated explicit RMT2 lift for GUE Airy model two-point correlations.
Conclusions:
- Proposed RMT2 as the framework for semiclassical amplitudes of off-shell n-boundary torus wormholes in AdS3 pure gravity.
- Identified a matching gravity calculation for the three-boundary case.
- RMT2 provides a powerful tool for studying quantum gravity phenomena.
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