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Register a new userHolographic Renyi relative divergence in JT gravity
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Authors
Tomonori Ugajin
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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.
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We perform a detailed analysis of holographic entanglement Renyi entropy in some modified theories of gravity with four dimensional conformal field theory duals. First, we construct perturbative black hole solutions in a recently proposed model of Einsteinian cubic gravity in five dimensions, and compute the Renyi entropy as well as the scaling dimension of the twist operators in the dual field theory. Consistency of these results are verified from the AdS/CFT correspondence, via a corresponding computation of the Weyl anomaly on the gravity side. Similar analyses are then carried out for three other examples of modified gravity in five dimensions that include a chemical potential, namely Born-Infeld gravity, charged quasi-topological gravity and a class of Weyl corrected gravity theories with a gauge field, with the last example being treated perturbatively. Some interesting bounds in the dual conformal field theory parameters in quasi-topological gravity are pointed out. We also provide arguments on the validity of our perturbative analysis, whenever applicable.
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 construct a new class of entanglement measures by extending the usual definition of Renyi entropy to include a chemical potential. These charged Renyi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFTs with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Renyi entropies in free field theories.
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.
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 $S_0$.
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