Modular-invariant random matrix theory and AdS${}_3$ wormholes
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917091021422592 |
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| author | Boruch, Jan Di Ubaldo, Gabriele Haehl, Felix M. Perlmutter, Eric Rozali, Moshe |
| author_facet | Boruch, Jan Di Ubaldo, Gabriele Haehl, Felix M. Perlmutter, Eric Rozali, Moshe |
| contents | We develop a non-perturbative definition of RMT${}_2$: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its $n$-point spectral correlations admit a prescribed modular-invariant lift to RMT${}_2$, 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 $\text{SL}(2,\mathbb{Z})$ spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT${}_2$ lift of two-point correlations of the GUE Airy model. We propose that in AdS$_3$ pure gravity, semiclassical amplitudes for off-shell $n$-boundary torus wormholes with topology $Σ_{0,n} \times S^1$ are given by the RMT${}_2$ lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT${}_2$ result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modular-invariant random matrix theory and AdS${}_3$ wormholes Boruch, Jan Di Ubaldo, Gabriele Haehl, Felix M. Perlmutter, Eric Rozali, Moshe High Energy Physics - Theory Chaotic Dynamics We develop a non-perturbative definition of RMT${}_2$: a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its $n$-point spectral correlations admit a prescribed modular-invariant lift to RMT${}_2$, 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 $\text{SL}(2,\mathbb{Z})$ spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT${}_2$ lift of two-point correlations of the GUE Airy model. We propose that in AdS$_3$ pure gravity, semiclassical amplitudes for off-shell $n$-boundary torus wormholes with topology $Σ_{0,n} \times S^1$ are given by the RMT${}_2$ lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT${}_2$ result. |
| title | Modular-invariant random matrix theory and AdS${}_3$ wormholes |
| topic | High Energy Physics - Theory Chaotic Dynamics |
| url | https://arxiv.org/abs/2503.00101 |