Low-temperature entropy in JT gravity

Abstract

For ensembles of Hamiltonians that fall under the Dyson classification of random matrices with $\beta \in \{1,2,4\}$, the low-temperature mean entropy can be shown to vanish as $⟨S(T)⟩\sim \kappa T^{\beta +1}$. A similar relation holds for Altland-Zirnbauer ensembles. JT gravity has been shown to be dual to the double-scaling limit of a $\beta =2$ ensemble, with a classical eigenvalue density $\propto e^{S_0}\sqrt{E}$ when $0<E\ll 1$. We use universal results about the distribution of the smallest eigenvalues in such ensembles to calculate $\kappa$ up to corrections that we argue are doubly exponentially small in $S_0$.

arXiv comment17 pages

References in corpus (17)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Level-Spacing Distributions and the Airy Kernel
• On Orthogonal and Symplectic Matrix Ensembles
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• Fermionic Localization of the Schwarzian Theory
• Level-Spacing Distributions and the Bessel Kernel
• JT gravity as a matrix integral
• Free Energy from Replica Wormholes
• JT gravity, KdV equations and macroscopic loop operators
• Explorations of Non-Perturbative JT Gravity and Supergravity
• Near-extreme eigenvalues and the first gap of Hermitian random matrices
• Joint distribution of the first and second eigenvalues at the soft edge of unitary ensembles
• Low Energy Thermodynamics of JT Gravity and Supergravity
• Replica symmetry breaking in random matrix model: a toy model of wormhole networks
• Quenched free energy in random matrix model
• Asymptotics of the Airy-kernel determinant
• The Distribution of the first Eigenvalue Spacing at the Hard Edge of the Laguerre Unitary Ensemble

Cited by in corpus (8)

• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
• Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity
• A Matrix Model for Flat Space Quantum Gravity
• Gravity as an ensemble and the moment problem
• Wigner meets 't Hooft near the black hole horizon
• Quantum Gravity Microstates from Fredholm Determinants
• A Black Hole Airy Tail
• Replicas for Random Matrices