Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLow-temperature entropy in JT gravity
67
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic 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 $langle S(T)ranglesim kappa T^{beta+1}$. 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 $S_0$.
rate research
Read More
Aspects of the low energy physics of certain Jackiw-Teitelboim gravity and supergravity theories are explored, using their recently presented non-perturbative description in terms of minimal string models. This regime necessarily involves non-perturbative phenomena, and the inclusion of wormhole geometries connecting multiple copies of the nearly AdS$_2$ boundary in the computation of ensemble averages of key quantities. A new replica-scaling limit is considered, combining the replica method and double scaling with the low energy limit. Using it, the leading free energy, entropy, and specific heat are explored for various examples. Two models of particular note are the JT supergravity theory defined as a (1,2) Altland-Zirnbauer matrix ensemble by Stanford and Witten, and the Saad-Shenker-Stanford matrix model of ordinary JT gravity (non-perturbatively improved at low energy). The full models have a finite non-vanishing spectral density at zero energy. The replica-scaling construction suggests for them a low temperature entropy and specific heat that are linear in temperature.
Recently, Saad, Shenker and Stanford showed how to define the genus expansion of Jackiw-Teitelboim quantum gravity in terms of a double-scaled Hermitian matrix model. However, the models non-perturbative sector has fatal instabilities at low energy that they cured by procedures that render the physics non-unique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical perturbative physics at high energy that instead has a stable and unambiguous non-perturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this non-perturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity.
We continue the systematic study of the thermal partition function of Jackiw-Teitelboim (JT) gravity started in [arXiv:1911.01659]. We generalize our analysis to the case of multi-boundary correlators with the help of the boundary creation operator. We clarify how the Korteweg-de Vries constraints arise in the presence of multiple boundaries, deriving differential equations obeyed by the correlators. The differential equations allow us to compute the genus expansion of the correlators up to any order without ambiguity. We also formulate a systematic method of calculating the WKB expansion of the Baker-Akhiezer function and the t Hooft expansion of the multi-boundary correlators. This new formalism is much more efficient than our previous method based on the topological recursion. We further investigate the low temperature expansion of the two-boundary correlator. We formulate a method of computing it up to any order and also find a universal form of the two-boundary correlator in terms of the error function. Using this result we are able to write down the analytic form of the spectral form factor in JT gravity and show how the ramp and plateau behavior comes about. We also study the Hartle-Hawking state in the free boson/fermion representation of the tau-function and discuss how it should be related to the multi-boundary correlators.
We holographically compute the Renyi relative divergence $D_{alpha} (rho_{+} || rho_{-})$ between two density matrices $rho_{+}, ; rho_{-}$ prepared by path integrals with constant background fields $lambda_{pm}$ coupled to a marginal operator in JT gravity. Our calculation is non perturbative in the difference between two sources $ lambda_{+} -lambda_{-}$. When this difference is large, the bulk geometry becomes a black hole with the maximal temperature allowed by the Renyi index $alpha$. In this limit, we find an analytic expression of the Renyi relative divergence, which is given by the on shell action of the back reacted black hole plus the contribution coming from the discontinuous change of the background field.
In this note, we consider the question of classicality for the theory which is known to be the effective description of two-dimensional black holes - the Morse quantum mechanics. We calculate the Wigner function and the Fisher information characterizing classicality/quantumness of single-particle systems and briefly discuss further directions to study.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
