An integrable road to a perturbative plateau

Abstract

As has been known since the 90s, there is an integrable structure underlying two-dimensional gravity theories. Recently, two-dimensional gravity theories have regained an enormous amount of attention, but now in relation with quantum chaos - superficially nothing like integrability. In this paper, we return to the roots and exploit the integrable structure underlying dilaton gravity theories to study a late time, large $e^{S_{\text{BH}}}$ double scaled limit of the spectral form factor. In this limit, a novel cancellation due to the integrable structure ensures that at each genus $g$ the spectral form factor grows like $T^{2g+1}$, and that the sum over genera converges, realising a perturbative approach to the late-time plateau. Along the way, we clarify various aspects of this integrable structure. In particular, we explain the central role played by ribbon graphs, we discuss intersection theory, and we explain what the relations with dilaton gravity and matrix models are from a more modern holographic perspective.

44 pages + appendices

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• Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
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• Non-perturbative Overlaps in JT Gravity: From Spectral Form Factor to Generating Functions of Complexity
• Spectral form factor in the $\tau$-scaling limit
• Symmetries and spectral statistics in chaotic conformal field theories II: Maass cusp forms and arithmetic chaos
• Aspects of $T\bar{T}+J\bar{T}$ deformed Schwarzian: From gravity partition function to late-time spectral form factor
• Les Houches lectures on two-dimensional gravity and holography
• Modular-invariant random matrix theory and AdS${}_3$ wormholes
• Universal Time Evolution of Holographic and Quantum Complexity
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• KdV conformal symmetry breaking in nearly AdS${}_2$
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• What happens due to the baby universe effect in JT gravity? -Analysis of correlation functions and ERB length at late time using three approaches-
• Chaos and moduli space volumes in unorientable JT gravity
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• Asymptotics of Weil-Petersson volumes and two-dimensional quantum gravities
• Topological gravity for arbitrary Dyson index
• Beyond the ensemble paradigm in low dimensional quantum gravity: Schwarzian density, quantum chaos and wormhole contributions
• The universality class of the first levels in low-dimensional gravity