arXiv subjects

Gabriele Di Ubaldo

Publications and source records attributed to Gabriele Di Ubaldo.

7 recordsLinked to original sources

arXiv2026

When the gravity path integral describes a statistical average

We find the necessary and sufficient conditions for the gravitational path integral (GPI) to admit an interpretation in terms of (i) an inner product in the Hilbert space of open/closed universes or (ii) a statistical average of boundary observables. The conditions needed for (i) are necessary but not sufficient for (ii). Requiring the stronger condition (ii) places additional constraints on all wormhole amplitudes, giving a concrete diagnostic of whether the GPI computes an average or merely a pseudo-average. To exemplify the difference between the two constraints, we present a class of gravitational toy models that satisfy (i) but fail the stronger condition (ii); to emphasize the power of the stronger condition, we initiate a bootstrap study of statistical ensembles based on condition (ii), finding that the resulting constraints substantially sharpen the bounds on the moments of the ensemble obtained by imposing (i). More broadly, both of these positivity conditions impose nontrivial constraints on wormhole amplitudes and thereby restrict which gravitational effective field theories can be embedded in consistent theories of quantum gravity.

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arXiv2026

Positivity of the gravitational path integral implies the axionic weak gravity conjecture

The gravitational path integral can compute inner products between different states of open and closed universes. To have a well-defined Hilbert space, these inner products should be positive semi-definite, which is not manifest in the low-energy effective theory. In this letter, we analyze the constraints that the positivity of inner products imposes on gravitational theories coupled to axions. If the axion has an exact shift symmetry, we show that, under mild assumptions, a combined positivity constraint on closed and open universes is violated when one includes certain wormholes. In low-energy effective theories where these wormholes are perturbatively stable, positivity requires that the wormholes have a non-perturbative instability that breaks the shift symmetry. This leads to a sharp version of the axion weak gravity conjecture, including precise numerical constants. We relate the bound to possible extensions of other swampland conjectures, arguing for an imaginary continuation of the distance conjecture. We comment on how the bound applies to axions in string theory and discuss phenomenological implications.

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arXiv2025

Modular-invariant random matrix theory and AdS${}_3$ wormholes

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.

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arXiv2025

Mind the crosscap: $τ$-scaling in non-orientable gravity and time-reversal-invariant systems

Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic CFTs, this is mirrored by the presence of non-orientable geometries in the dual gravitational path integral. In this work, we analyze general properties of these matrix models and their gravitational counterparts. First, we develop a formalism to express the universal level statistics in the canonical ensemble for arbitrary spectral curves, leading to a topological expansion with finite radius of convergence in the late-time $τ$-scaling limit. Then, we focus on topological gravity and study topological recursion on the moduli space of non-orientable surfaces. We find that the Weil-Petersson volumes display non-analytic behaviour multiplying polynomials in the boundary lengths. The volumes give rise to wormholes with late-time divergences, in contrast with the orientable case, which is finite. We identify systematic cancellations among WP volumes implied by the consistency and finiteness of the $τ$-scaling limit. In particular, the cancellation of late-time divergences requires a nontrivial genus resummation. Working in the gravitational microcanonical ensemble, we derive and resum all orders of the topological expansion matching the GOE matrix model in the high-energy regime.

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arXiv2023

AdS$_3$/RMT$_2$ Duality

We introduce a framework for quantifying random matrix behavior of 2d CFTs and AdS$_3$ quantum gravity. We present a 2d CFT trace formula, precisely analogous to the Gutzwiller trace formula for chaotic quantum systems, which originates from the $SL(2,\mathbb{Z})$ spectral decomposition of the Virasoro primary density of states. An analogy to Berry's diagonal approximation allows us to extract spectral statistics of individual 2d CFTs by coarse-graining, and to identify signatures of chaos and random matrix universality. This leads to a necessary and sufficient condition for a 2d CFT to display a linear ramp in its coarse-grained spectral form factor. Turning to gravity, AdS$_3$ torus wormholes are cleanly interpreted as diagonal projections of squared partition functions of microscopic 2d CFTs. The projection makes use of Hecke operators. The Cotler-Jensen wormhole of AdS$_3$ pure gravity is shown to be extremal among wormhole amplitudes: it is the minimal completion of the random matrix theory correlator compatible with Virasoro symmetry and $SL(2,\mathbb{Z})$-invariance. We call this MaxRMT: the maximal realization of random matrix universality consistent with the necessary symmetries. Completeness of the $SL(2,\mathbb{Z})$ spectral decomposition as a trace formula allows us to factorize the Cotler-Jensen wormhole, extracting the microscopic object $Z_{\rm RMT}(τ)$ from the coarse-grained product. This captures details of the spectrum of BTZ black hole microstates. $Z_{\rm RMT}(τ)$ may be interpreted as an AdS$_3$ half-wormhole. We discuss its implications for the dual CFT and modular bootstrap at large central charge.

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arXiv2023

AdS$_3$ Pure Gravity and Stringy Unitarity

We construct a unitary, modular-invariant torus partition function of a two-dimensional conformal field theory with a Virasoro primary spectral gap of $Δ_* = \frac{c-1}{12}$ above the vacuum. The twist gap is identical, apart from two states $\mathcal{O}_*$ with spin scaling linearly in the central charge $c$. These states admit an AdS$_3$ interpretation as strongly coupled strings. All other states are black hole microstates.

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arXiv2023

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

We consider the generalization of a matrix integral with arbitrary spectral curve $ρ_0(E)$ to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-$N$, we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around $ρ_0(E)$, which is now the large-$N$ limit of the quantum expectation value of the eigenvalue density operator $\hatρ(E)$. The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a $\textit{one-time-point}$ reduction of MQM. As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the $c=1$ matrix model dual to two-dimensional string theory and extend it to arbitrary $ρ_0(E)$. The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of $n<N$ eigenvalues.

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