Modular-invariant random matrix theory and AdS3 wormholes
Modular-invariant random matrix theory and AdS3 wormholes
We develop a non-perturbative definition of RMT: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its -point spectral correlations admit a prescribed modular-invariant lift to RMT, which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT lift of two-point correlations of the GUE Airy model. We propose that in AdS pure gravity, semiclassical amplitudes for off-shell -boundary torus wormholes with topology are given by the RMT lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT result.
Boruch, Jan
486260ad-5e1b-483f-9f2f-1c3ab734f3a1
Di Ubaldo, Gabriele
5062cc4c-63f8-448f-91be-6b668f21ebfd
Haehl, Felix
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Perlmutter, Eric
f0eeffab-4baa-4bb0-bcbd-4ea6c1f05329
Rozali, Moshe
e2227ff5-1a36-43d4-bc32-0a0dc5bd2523
18 September 2025
Boruch, Jan
486260ad-5e1b-483f-9f2f-1c3ab734f3a1
Di Ubaldo, Gabriele
5062cc4c-63f8-448f-91be-6b668f21ebfd
Haehl, Felix
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Perlmutter, Eric
f0eeffab-4baa-4bb0-bcbd-4ea6c1f05329
Rozali, Moshe
e2227ff5-1a36-43d4-bc32-0a0dc5bd2523
Boruch, Jan, Di Ubaldo, Gabriele, Haehl, Felix, Perlmutter, Eric and Rozali, Moshe
(2025)
Modular-invariant random matrix theory and AdS3 wormholes.
arXiv, 135.
(doi:10.48550/arXiv.2503.00101).
Abstract
We develop a non-perturbative definition of RMT: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its -point spectral correlations admit a prescribed modular-invariant lift to RMT, which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT lift of two-point correlations of the GUE Airy model. We propose that in AdS pure gravity, semiclassical amplitudes for off-shell -boundary torus wormholes with topology are given by the RMT lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT result.
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2503.00101v1
- Author's Original
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4hhn-c6mp
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Accepted/In Press date: 7 August 2025
Published date: 18 September 2025
Identifiers
Local EPrints ID: 505590
URI: http://eprints.soton.ac.uk/id/eprint/505590
ISSN: 2331-8422
PURE UUID: dcd10ac6-3066-4caa-967e-dd7064f1f76a
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Date deposited: 14 Oct 2025 16:44
Last modified: 15 Oct 2025 02:08
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Author:
Jan Boruch
Author:
Gabriele Di Ubaldo
Author:
Felix Haehl
Author:
Eric Perlmutter
Author:
Moshe Rozali
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