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

We present a comprehensive analytical study of a variation of the eigenvector ensemble initially proposed by Deutsch [1, 2] for the foundations of the Eigenstate Thermalization Hypothesis (ETH). This ensemble, called the $\textit{C}$-ensemble, incorporates additional system-dependent information, enabling the study of complex quantum systems beyond the universal predictions of Random Matrix Theory (RMT). Specifically, we focus on how system-specific details influence late-time behavior in correlation functions, such as the spectral form factor, and how explicit Hamiltonian corrections not captured by RMT can be included. We demonstrate the consistency of this ensemble with respect to the universal (Haar) results by showing that it defines a unitary 1-design for arbitrary systems and for strongly chaotic systems it becomes an approximated 2-design. Universal expressions for two- and four-point ensemble-averaged correlation functions are derived, revealing how system-dependent information is spectrally decoupled. Furthermore, we show that for small energy windows, the correlation functions defined by this ensemble reduce to the predictions made by the ETH.

Colombia

Brazil

William Salazar

Javier Madroñero

On a matrix ensemble for arbitrary complex quantum systems

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

Fabian Haneder

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

The constituent quark model is used to compute the ground and excited state masses of QQQbaryons containing either c or bquarks. The quark model parameters previously used to describe the properties of charmonium and bottomonium states were used in this analysis. The non-relativistic three-body bound state problem is solved by means of the Gaussian expansion method which provides sufficient accuracy and simplifies the subsequent evaluation of the matrix elements. Several low-lying states with quantum numbers 
					 and 
					 are reported. We compare the results with those obtained by the other theoretical formalisms. There is a general agreement for the mass of the ground state in each sector of triply heavy baryons. However, the situation is more puzzling for the excited states, and appropriate comments about the most relevant features of our comparison are given.
				

China

Gang Yang

Jialun Ping

Spain

Pablo G. Ortega

Jorge Segovia

Triply heavy baryons in the constituent quark model Supported by China Postdoctoral Science Foundation (2019M650617), National Natural Science Foundation of China (11535005, 11775118), and by Spanish Ministerio de Economía, Industria y Competitividad under contractsno. FPA2017-86380-P and FPA2016-77177-C2-2-P. P.G.O. acknowledges the financial support from Spanish MINECO's Juan de la Cierva-Incorporación programme, Grant Agreement No. IJCI-2016-28525.