We show the late time, or $\textit{τ–}$scaled, limit of the canonical spectral form factor (SFF) in unorientable JT gravity agrees with universal random matrix theory (RMT) up to genus one in the topological expansion, establishing a key signature of quantum chaos for the time-reversal symmetric case. The loop equations for an orthogonal matrix model with spectral curve $\textit{y}$($\textit{z}$) ∝ sin(2$\textit{πz}$) are used to compute the moduli space volumes of unorientable surfaces. The divergences of the unorientable volumes are regularized by first regularizing the resolvents of the orthogonal matrix model. To this end, we make use of the large $\textit{p}$ limit of the (2$\textit{,}$ 2$\textit{p}$ + 1) minimal string model. Using properties of the volumes and the loop equations, we derive streamlined formulas to compute the volumes for one and two boundaries, giving explicit results up to genus one. We find the general structure of the unorientable volumes to be written in terms of multiple polylogarithms and zeta values, with weight determined by the genus, number of boundaries, and number of crosscaps. In the $\textit{τ–}$scaled limit, contributions to the SFF from the divergent parts of the volume cancel, and the SFF becomes finite and independent of regularization. The SFF from universal RMT is a distinct computation, that depends on the leading order energy density of JT gravity, which we also derive up to genus one.

United States

Jarod Tall

Germany

Torsten Weber

Juan Urbina

Klaus Richter

Chaos and moduli space volumes in unorientable JT gravity

Based on periodic orbit theory, we address the individual-system versus ensemble interpretation of quantum gravity from a quantum chaos perspective. To this end, we show that the spectrum of geodesic motion on high-dimensional hyperbolic manifolds, described by the Selberg trace formula, displays a Schwarzian (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>sinh</mi><mn>2</mn><mi>π</mi><msqrt><mi>E</mi></msqrt></math>) mean level density. Due to its chaotic classical limit, this quantum system also shows all universal signatures of quantum chaos. These two properties imply a possible duality to Jackiw-Teitelboim-type quantum gravity at the level of a single system instead of an ensemble of systems like matrix- and Sachdev-Ye-Kitaev models. Moving beyond the universal regime, we show how the full wormhole geometry on the gravity side emerges from the discreteness of the set of periodic orbits. Thereby, we take initial steps towards a duality between gravitational and mesoscopic chaotic quantum systems through the topological, respectively, periodic orbit expansions of their correlators.

Fabian Haneder

Juan Diego Urbina

Camilo Moreno

Beyond the ensemble paradigm in low-dimensional quantum gravity: Schwarzian density, quantum chaos, and wormhole contributions

When a gravitational wave (GW) passes through a dc magnetic field, it couples to the conducting wires carrying the currents which generate the magnetic field, causing them to oscillate at the GW frequency. The oscillating currents then generate an ac component through which the GW can be detected—thus forming a resonant mass detector or a nagnetic Weber bar. We quantify this claim and demonstrate that magnets can have exceptional sensitivity to GWs over a frequency range demarcated by the mechanical and electromagnetic resonant frequencies of the system; indeed, we outline why a magnetic readout strategy can be considered an optimal Weber bar design. The concept is applicable to a broad class of magnets, but can be particularly well exploited by the powerful magnets being deployed in search of axion dark matter, for example, by DMRadio and ADMX-EFR. Explicitly, we demonstrate that the MRI magnet that is being deployed for ADMX-EFR can achieve a broadband GW strain sensitivity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>20</mn></mrow></msup><mo>/</mo><msqrt><mi>Hz</mi></msqrt></math> from a few kHz to about 10 MHz, with a peak sensitivity down to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>22</mn></mrow></msup><mo>/</mo><msqrt><mi>Hz</mi></msqrt></math> at a kHz exploiting a mechanical resonance.

CERN

Valerie Domcke

Switzerland

Sebastian A.R. Ellis

Nicholas L. Rodd

Magnets are Weber Bar Gravitational Wave Detectors

A correction to this paper has been published: https://doi.org/10.1007/JHEP07(2024)267

Erratum to: Unorientable topological gravity and orthogonal random matrix universality

The duality of Jackiw-Teitelboim (JT) gravity and a double scaled matrix integral has led to studies of the canonical spectral form factor (SFF) in the so called τ−scaled limit of large times, t → ∞, and fixed temperature, in order to demonstrate agreement with universal random matrix theory (RMT). Though this has been established for the unitary case, extensions to other symmetry classes requires the inclusion of unorientable manifolds in the sum over geometries, necessary to address time reversal invariance, and regularization of the corresponding prime geometrical objects, the Weil-Petersson (WP) volumes. We report here how universal signatures of quantum chaos, witnessed by the fidelity to the Gaussian orthogonal ensemble, emerge for the low-energy limit of unorientable JT gravity, i.e. the unorientable Airy model/topological gravity. To this end, we implement the loop equations for the corresponding dual (double-scaled) matrix model and find the generic form of the unorientable Airy WP volumes, supported by calculations using unorientable Kontsevich graphs. In an apparent violation of the gravity/chaos duality, the τ−scaled SFF on the gravity side acquires both logarithmic and power law contributions in t, not manifestly present on the RMT side. We show the expressions can be made to agree by means of bootstrapping-like relations hidden in the asymptotic expansions of generalized hypergeometric functions. Thus, we are able to establish strong evidence of the quantum chaotic nature of unorientable topological gravity.

Unorientable topological gravity and orthogonal random matrix universality

A gravitational wave (GW) passing through a pulsar will lead to a variation in the moment of inertia of the pulsar affecting its rotation. This will affect the extremely accurately measured spin rate of the pulsar as well as its pulse profile (due to induced wobbling depending on the source direction). The effect will be most pronounced at resonance and should be detectable by accurate observations of the pulsar signal. The pulsar, in this sense, acts as a remotely stationed Weber detector of gravitational waves whose signal can be monitored on earth. With possible GW sources spread around in the universe, pulsars in their neighborhoods can provide us a family of remote detectors all of which can be monitored on earth. Even if GW are detected directly by earth based conventional detectors, such pulsar detectors can provide additional information for accurate determination of the source location. This can be of crucial importance for sources which do not emit any other form of radiation such as black hole mergers. For the GW events already detected by LIGO (and Virgo), we propose that one should look for specific pulsars which would have been disturbed by these events, and will transmit this disturbance via their pulse signals in any foreseeable future. One should be able to predict these future pulsar events with some accuracy so that a focused effort can be made to detect any possible changes in the signals of those specific pulsars.