AdS Background Research Articles

Worldsheet kinematics, dressing factors and odd crossing in mixed-flux AdS3 backgrounds

String theory on AdS3 × S3 × T4 geometries supported by a combination of NS-NS and R-R charges is believed to be integrable. We elucidate the kinematics and analytic structure of worldsheet excitations in mixed charge and pure NS-NS backgrounds, when expressed in momentum, Zhukovsky variables and the rapidity u which appears in the quantum spectral curve. We discuss the relations between fundamental and bound state excitations and the role of fusion in constraining and determining the S matrices of these theories. We propose a scalar dressing factor consistent with a novel u-plane periodicity and comment on its close relation to the XXZ model at roots of unity. We solve the odd part of crossing and show that our solution is consistent with fusion and reduces in the relativistic limit to dressing phases previously found in the literature.

Asymptotic symmetries from the string worldsheet

In IIB string theory on AdS3 background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the asymptotic boundary of the target spacetime. The charges on the worldsheet that generate the corresponding transformations can be written down in both the Lagrangian formalism and Hamiltonian formalism. This provides a method of studying asymptotic symmetry of the target spacetime directly from worldsheet string theories, without using results from the supergravity limit. As an example, we apply this method to flat spacetime in three dimensions and obtain the BMS3 generators on the worldsheet theory.

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

Modular average and Weyl anomaly in two-dimensional Schwarzian theory

The gauge formulation of Einstein gravity in AdS3 background leads to a boundary theory that breaks modular symmetry and loses the covariant form. We examine the Weyl anomaly for the cylinder and torus manifolds. The divergent term is the same as the Liouville theory when transforming from the cylinder to the sphere. The general Weyl transformation on the torus also reproduces the Liouville theory. The Weyl transformation introduces an additional boundary term for reproducing the Liouville theory, which allows the use of CFT techniques to analyze the theory. The torus partition function in this boundary theory is one-loop exact, and an analytical solution to disjoint two-interval Rényi-2 mutual information can be obtained. We also discuss a first-order phase transition for the separation length of two intervals, which occurs at the classical level but is smoothed out by non-perturbative effects captured by averaging over a modular group in the boundary theory.

Spin-2 universal minimal solutions on type IIA and IIB supergravity

In this paper, we consider the spin-2 field perturbations of four families of supergravity solutions. These include AdS5 and AdS7 backgrounds of type IIA as well as AdS4 and AdS6 backgrounds of Type IIB. As the main result, we show that, in all the cases, there is a solution given by a combination of the warp factors. We also find the respective mass spectra. We analyze the normalizability of the solutions and identify the superconformal multiplets dual to them.

Strange higher-spin topological systems in 3D

Motivated by the generation of action principles from off-shell dualisation, we present a general class of free, topological theories in three dimensional Minkowski spacetime that exhibit higher-spin gauge invariance. In the spin-two case, we recover a dual reformulation of the triplet system already known, while the higher-spin systems that we obtain seem to be new. They are associated with wild quivers. We study in which situations these exotic (or strange) higher-spin models can be extended to dS3 and AdS3 backgrounds, revealing that the flat limit of such models, when they exist, admits a one-parameter freedom. Interactions are studied in the simplest higher-spin case featuring spin-2 and spin-3 fields. We then give several higher-spin generalizations of these strange systems.

Real time holography for higher spin theories

Real time holography is studied in the context of the embedding space formalism. In the first part of this paper, we present matching conditions for on-shell integer spin fields when going from Euclidean to Lorentzian signature on AdS background. Using the BTZ black hole as an example, we discuss various ways of lifting the physical solution from the AdS surface to the whole embedding space. The BTZ propagator for higher spin field is expressed elegantly in terms of the embedding coordinates. In the second part of the paper, we develop the proposed duality between higher spin theory and vector models. We obtain a specific map between the field configurations of these two theories in real time, so called Lorentzian AdS/CFT map. We conclude by exploring the matching conditions for higher spin fields satisfying the proposed bulk quadratic action. The physical and ghost modes can be treated independently during the Wick rotation; only physical modes are considered to be external modes.

Holography and correlation functions of huge operators: spacetime bananas

We initiate the study of holographic correlators for operators whose dimension scales with the central charge of the CFT. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincaré boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as “spacetime bananas”. As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.

DS4 universe emergent from Kerr-AdS5 spacetime: bubble nucleation catalyzed by a black hole

The emergence of a four-dimensional de Sitter (dS4) universe on an expanding bubble in the five-dimensional anti-de Sitter (AdS5) background has been suggested as a possible cosmological scenario. It is motivated by the difficulties in the realization of a stable de Sitter vacua in string theory. The bubble can be nucleated in a meta-stable pure AdS5 spacetime, but it is known that a pure AdS spacetime is non-perturbatively unstable. It means that the pure AdS5 background is an idealized situation, and in realistic situations, non-linear perturbations in AdS may lead to the formation of black holes due to the gravitational turbulent instability. To investigate how the proposed scenario works in a more realistic situation, we here study the nucleation process of a vacuum bubble in the Kerr-AdS5 spacetime. Especially we investigate conditions sufficient to ensure the nucleation of a vacuum bubble with a rotating black hole and how the black hole affects the transition rate. We find that even in the Kerr-AdS5 spacetime, a quasi-dS4 expansion can be realized on the nucleated vacuum bubble without contradicting the de Sitter swampland conjectures.

Bi-η and bi-λ deformations of ℤ4 permutation supercosets

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

Einstein-scalar field solutions in AdS spacetime: clouds, boundary conditions, and scalar multipoles

We consider an Einstein-scalar field model which is a consistent truncation of mathcal{N} = 8 D = 4 gauged supergravity, the scalar field possessing a potential which is unbounded from below and a tachyonic mass above the Breitenlohner-Freedman bound. We investigate the spherically symmetric asymptotically anti-de Sitter soliton and black hole solutions, with the aim of clarifying the asymptotics and the possible boundary conditions at infinity. The emerging picture is contrasted with that found for an Einstein-scalar field model with the same scalar mass and a quartic selfinteraction term. We also provide arguments for the existence of solitonic solutions which can be viewed as non-linear continuation of the (probe) scalar multipolar clouds, with emphasis on the dipole case. Apart from numerical results, exact solutions are found for solitons with a monopole and dipole scalar field, as perturbations around the AdS background.

Nonsingular black hole chemistry in 4D Einstein-Gauss-Bonnet gravity

The EGB is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in D>4 dimensions, and EGB gravity is topologically invariant in 4D. Several ways have been proposed for regularizing the D→4 limit of EGB for non-trivial gravitational dynamics in 4D. Motivated by the importance of AdS/CFT, we obtain an exact static spherically symmetric nonsingular black hole in 4D EGB gravity coupled to the nonlinear electrodynamics (NED) in an AdS spacetime. We interpret the negative cosmological constant Λ as the positive pressure, via P=−Λ/8π, of the system's thermodynamic properties of the nonsingular black hole with an AdS background. We find that for P<Pc, the black holes with CP>0 are stable to thermal fluctuations and unstable otherwise. We also analyzed the Gibbs free energy to find that the small globally unstable black holes undergo a phase transition to the large globally stable black holes. Further, we study the P−V criticality of the system and then calculate the critical exponents to find that our system behaves like Van der Walls fluid.

Thermodynamics of a quantum corrected Schwarzschild black hole in AdS spacetime

The thermodynamics for a quantum corrected Schwarzschild black hole with AdS background is investigated. First, the black hole metric is introduced and given when the spherical symmetric quantum fluctuations of spacetime are considered for Schwarzschild AdS black hole. Then, based on AdS background, we get the free energy for the quantum corrected black hole by AdS gravity renormalization and saddle-point approximation. By the spherical symmetric quantum fluctuation in AdS spacetime is considered, there are three main results found. Firstly, due to quantum fluctuation, there is a divergence term in the Euclidean action, which contributes to the energy of spacetime. Secondly, the entropy of the modified black hole is still proportional to the horizon area. But when the contribution of quantum fluctuations is deducted, the relationship between entropy and area is not so. It shows that, the area entropy theorem for the black hole is the both effect of quantum fluctuations and black hole. Thirdly, quantum fluctuation doesn't affect the temperature of Hawking-Page transition, but the radius of the black hole of Hawking-Page transition will be corrected.

Generalised U-dual solutions in supergravity

We discuss the notion of generalised U-duality as a solution generating technique in supergravity. We demonstrate a method to take solutions of type IIA supergravity on a 3-sphere, with NSNS flux, to new solutions of 11-dimensional supergravity, using exceptional geometry techniques. These new solutions are characterised by an underlying 3-algebra structure, and generalise features of solutions obtained by non-abelian T-duality, which involve an underlying ordinary Lie algebra. We focus on an example where we start with the pp-F1-NS5 solution in type IIA supergravity. We discuss the properties of our resulting new solution, including the possibility of viewing it globally as a U-fold, and its M2 and M5 brane charges. In the extremal case, the new solution admits an AdS3 limit, which falls into a recently constructed class of M-theory AdS3 backgrounds — this provides a global completion of our solution with a well-defined holographic dual, similar to the global completions of non-abelian T-dual solutions. Our full solution is a 6-vector deformation of this AdS3 limit. We also explicitly solve the Killing spinor equation in the AdS3 limit, finding a frac{1}{2}hbox{-} mathrm{BPS} solution.

Light deflection angle by superentropic black holes

Motivated by recent works on light deflection and shadow behaviors on AdS geometries [S. Haroon, M. Jamil, K. Jusufi, K. Lin and R. B. Mann, Phys. Rev. D 99 (2019) 044015, arXiv:1810.04103; A. Belhaj, H. Belmahi and M. Benali, Phys. Lett. B 821 (2021) 136619, arXiv:2110.06771], we investigate the deflection angle of light rays by superentropic black holes. Taking appropriate approximations, we first obtain the involved expression. For large values of the impact parameter, we get a specific value being zero for ordinary black holes without AdS backgrounds. Then, we examine and analyze such an optical quantity by providing graphical discussions in terms of a bounded region of the moduli space required by superentropic black hole conditions. Concretely, we study the deflection angle aspects by varying the black hole mass being fixed in the previous findings.

The holographic space-time and black hole remnants as dark matter

The holographic space-time approach to inflation provides a well defined and self-contained framework to study the early universe. Based on a quasi-local quantum gravity theory generalizing string theory beyond AdS backgrounds, it addresses fundamental questions like the arrow of time and the entropy of the initial cosmological state. It was recently argued that it also provides a natural explanation for dark matter in the form of primordial black holes. The original idea however suffers from troubles that can be cured by considering instead Planck relics. This possibility is investigated and paths for observational confirmation are pointed out.

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Holographic entanglement entropy was recently recast in terms of Riemannian flows or ‘bit threads’. We consider the Lorentzian analog to reformulate the ‘complexity=volume’ conjecture using Lorentzian flows — timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or ‘gatelines’. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific ‘canonical’ thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein’s equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of ‘spacetime complexity’. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [1], including several new results.

Reflected entropy in double holography

Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge. In this paper, we study the reflected entropy in the doubly holographic setup, which contains the degrees of freedom of quantum matter in the bulk. In this context, we propose a notion of quantum entanglement wedge cross-section, which may describe the reflected entropy with higher-order quantum corrections. We numerically compute the reflected entropy in pure AdS background and black hole background in four dimensions, respectively. In general, the reflected entropy contains the contribution from the geometry on the brane and the contribution from the CFT. We compute their proportion for different Newton constants and find that their behaviors are in agreement with the results based on the semi-classical gravity and the correlation of CFT coupled to the bath CFT.

Asymptotically free AdS3/CFT2

We propose a new AdS3/CFT2 duality, in which the bulk string theory has a target spacetime AdS3 times a squashed three-sphere {mathbbm{S}}_{flat}^3 , and the dual CFT2 is a symmetric product of sigma models on ℝϕ× {mathbbm{S}}_{flat}^3 , deformed by a ϕ-dependent ℤ2 twist operator. The duality maps the asymptotic region of AdS3 to the region ϕ → ∞, where the twist interaction in the CFT2 turns off. The AdS3 backgrounds in question have RAdS< ℓs, and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS3 rather than an ensemble of BTZ black holes. This property allows us to derive the dual CFT2 by a systematic analysis of the worldsheet string theory on AdS3.

Deflection light behaviors by AdS black holes

We investigate the behavior of the deflection of light rays by charged and rotating AdS black holes using the Gauss–Bonnet formalism. Taking weak field approximations and certain appropriate limits associated with AdS geometries, we compute and analyze such an optical quantity by varying the involved moduli space parameters. First, we study the charge and the AdS radius effects on the deflection angle of RN-AdS black holes. For small values of the impact parameter b, we find that the charge effect is relevant. Precisely, it decreases the deflection angle, while the AdS background one is not. For large values of b, however, these optical behaviors have been inverted and the deflection angle becomes an increasing function of the charge. In this way, the cosmological constant effect is remarked to be relevant showing linear variations of the deflection angle. Varying the charge, we find a critical impact parameter value \(b_{c}\) where the charge effect is inverted. For rotating solutions, we show that the spinning parameter still decreases the deflection angle without any changing behavior observed in the charge effect. Evincing of the cosmological constant, we recover known results corresponding to charged and rotating ordinary black hole solutions. Examining the plasma effect, we reveal that the deflection angle keeps the same behavior being a decreasing function in terms of the frequency ratio.