Asymptotic AdS Boundary Research Articles

Factorizing wormholes in a partially disorder-averaged SYK model

In this paper, we introduce a “partially disorder-averaged” SYK model. This model has a real parameter that smoothly interpolates between the ordinary totally disorder-averaged SYK model and the totally fixed-coupling model. For the large N effective description, in addition to the usual bi-local collective fields, we also introduce a new additional set of local collective fields. These local fields can be understood as “half” of the bi-local collective fields, and in the totally fixed-coupling limit, they represent the “half-wormholes” which were found in recent studies. We find that the large N saddles of these local fields vanish in the total-disorder-averaged limit, while they develop nontrivial profiles as we gradually fix the coupling constants. We argue that the bulk picture of these local collective fields represents a correlation between a spacetime brane and the asymptotic AdS boundary. This illuminates how the half-wormhole saddles emerge in the SYK model with fixed couplings.

Effective entropy of quantum fields coupled with gravity

Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

A practical approach to the Hamilton-Jacobi formulation of holographic renormalization

We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general relativity, the actual application of our algorithm does not. The work applies to any $D$-dimensional holographic dual with asymptotic AdS boundary, Euclidean or Lorentzian, and arbitrary slicing. We illustrate the method in several examples, including the FGPW model, a holographic model of 3d ABJM theory, and cases with marginal scalars such as a dilaton-axion system.

Holographic entanglement entropy and thermodynamic instability of planarR-charged black holes

The holographic entanglement entropy of an infinite strip subsystem on the asymptotic AdS boundary is used as a probe to study the thermodynamic instabilities of planar R-charged black holes (or their dual field theories). We focus on the single-charge AdS black holes in $D=5$, which correspond to spinning D3-branes with one non-vanishing angular momentum. Our results show that the holographic entanglement entropy indeed exhibits the thermodynamic instability associated with the divergence of the specific heat. When the width of the strip is large enough, the finite part of the holographic entanglement entropy as a function of the temperature resembles the thermal entropy, as is expected. As the width becomes smaller, however, the two entropies behave differently. In particular, there exists a critical value for the width of the strip, below which the finite part of the holographic entanglement entropy as a function of the temperature develops a self-intersection. We also find similar behavior in the single-charge black holes in $D=4$ and $7$.

Holographic charged fluid with anomalous current at finite cutoff surface in Einstein-Maxwell gravity

The holographic charged fluid with anomalous current in Einstein-Maxwell gravity has been generalized from the infinite boundary to the finite cutoff surface by using the gravity/fluid correspondence. After perturbing the boosted Reissner-Nordstrom (RN)-AdS black brane solution of the Einstein-Maxwell gravity with the Chern-Simons term, we obtain the first order perturbative gravitational and Maxwell solutions, and calculate the stress tensor and charged current of the dual fluid at finite cutoff surfaces which contains undetermined parameters after demanding regularity condition at the future horizon. We adopt the Dirichlet boundary condition and impose the Landau frame to fix these parameters, finally obtain the dependence of transport coefficients in the dual stress tensor and charged current on the arbitrary radical cutoff $r_c$. We find that the dual fluid is not conformal, but it has vanishing bulk viscosity, and the shear viscosity to entropy density ratio is universally $1/4\pi$. Other transport coefficients of the dual current turns out to be cutoff-dependent. In particular, the chiral vortical conductivity expressed in terms of thermodynamic quantities takes the same form as that of the dual fluid at the asymptotic AdS boundary, and the chiral magnetic conductivity receives a cutoff-dependent correction which vanishes at the infinite boundary.

On the universal hydrodynamics of strongly coupled CFTs with gravity duals

It is known that the solutions of pure classical 5D gravity with AdS5 asymptotics can describe strongly coupled large N dynamics in a universal sector of 4D conformal gauge theories. We show that when the boundary metric is flat we can uniquely specify the solution by the boundary stress tensor. We also show that in the Fefferman-Graham coordinates all these solutions have an integer Taylor series expansion in the radial coordinate (i.e. no log terms). Specifying an arbitrary stress tensor can lead to two types of pathologies, it can either destroy the asymptotic AdS boundary condition or it can produce naked singularities. We show that when solutions have no net angular momentum, all hydrodynamic stress tensors preserve the asymptotic AdS boundary condition, though they may produce naked singularities. We construct solutions corresponding to arbitrary hydrodynamic stress tensors in Fefferman-Graham coordinates using a derivative expansion. In contrast to Eddington-Finkelstein coordinates here the constraint equations simplify and at each order it is manifestly Lorentz covariant. The regularity analysis, becomes more elaborate, but we can show that there is a unique hydrodynamic stress tensor which gives us solutions free of naked singularities. In the process we write down explicit first order solutions in both Fefferman-Graham and Eddington-Finkelstein coordinates for hydrodynamic stress tensors with arbitrary η/s. Our solutions can describe arbitrary (slowly varying) velocity configurations. We point out some field-theoretic implications of our general results.