Anti-de Sitter Research Articles

Holographic complexity in string and M theory

Thus far, the literature regarding holographic complexity almost entirely focuses on the context of (d+1)-dimensional anti–de Sitter spacetime rather than the full higher-dimensional gauge/gravity duality in string or M theory. We provide a framework to study holographic complexity in the full duality, explaining the relation of complexity functionals in the higher-dimensional theory to those in anti–de Sitter spacetime and when complexity functionals can apply universally to gauge/gravity dualities rather than a specific dual pair. We also show that gauge invariance constrains boundary terms for complexity functionals, using the 10- and 11-dimensional supergravity actions as key examples. Finally, we propose new universal complexity functionals following these considerations, including a revised gauge-invariant action complexity. Published by the American Physical Society 2025

Vacuum transitions with the Gauss-Bonnet term in D dimensions

In our previous paper [; ], we proposed a probabilistic argument to explain the reason why the cosmological constant is very small in 4D. We can ask a question: if the behavior of tunneling exponent B can be generalized to D-dimension. Moreover, in higher dimensional theory motivated by string theory the Gauss-Bonnet term plays an important role. Therefore, in this paper, we generalize our result in previous paper [; ] to arbitrary D dimensions including the Gauss-Bonnet term. As a result, we have two main results. We find that the Euclidean action of the bounce, B, describing the decay of a de Sitter vacuum, is proportional to k+−(D−2), which has a pole as k+2→0 where k+2 is the curvature of the parent vacuum. This result is similar to the result in 4D. The other result is that we find a new decay channel, describing up-tunneling from anti–de Sitter into de Sitter. The meaning of this new decay channel in the string landscape should be explored in the future. Published by the American Physical Society 2025

Probing hidden topology with quantum detectors

We consider the transition rate of a static Unruh-DeWitt detector in two (2+1)-dimensional black hole spacetimes that are isometric to the static Bañados-Teitelboim-Zanelli black hole outside the horizon but have no asymptotically locally anti–de Sitter exterior behind the horizon. The spacetimes are the RP2 geon, with spatial topology RP2\{point at infinity}, and the Swedish geon of Åminneborg ., with spatial topology T2\{point at infinity}. For a conformal scalar field, prepared in the Hartle-Hawking-type state that is induced from the global vacuum on the anti–de Sitter covering space, we show numerically that the detector’s transition rate distinguishes the two spacetimes, particularly at late exterior times, and we trace this phenomenon to the differences in the isometries that are broken by the quotient construction from the universal covering space. Our results provide an example in which information about the interior topology of a black hole is accessible to a quantum observer outside the black hole. Published by the American Physical Society 2025

Generalized Fefferman-Graham gauge and boundary Weyl structures

In the framework of AdS/CFT correspondence, the Fefferman-Graham (FG) gauge offers a useful way to express asymptotically anti-de Sitter spaces, allowing a clear identification of their boundary structure. A known feature of this approach is that choosing a particular conformal representative for the boundary metric breaks explicitly the boundary scaling symmetry. Recent developments have shown that it is possible to generalize the FG gauge to restore boundary Weyl invariance by adopting the Weyl-Fefferman-Graham gauge. In this paper, we focus on three-dimensional gravity and study the emergence of a boundary Weyl structure when considering the most general AdS boundary conditions introduced by Grumiller and Riegler [1]. We extend the holographic renormalization scheme to incorporate Weyl covariant quantities, identifying new subleading divergences appearing at the boundary. To address these, we introduce a new codimension-two counterterm, or corner term, that ensures the finiteness of the gravitational action. From here, we construct the quantum-generating functional, the holographic stress tensor, and compute the corresponding Weyl anomaly, showing that the latter is now expressed in a full Weyl covariant way. Finally, we discuss explicit applications to holographic integrable models and accelerating black holes. For the latter, we show that the new corner term plays a crucial role in the computation of the Euclidean on-shell action.

Conformal Solutions of Static Plane Symmetric Cosmological Models in Cases of a Perfect Fluid and a Cosmic String Cloud

In this work, we obtained exact solutions of Einstein’s field equations for plane symmetric cosmological models by assuming that they admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum and conformally flat. We have shown that in the case of a perfect fluid, these solutions have an energy-momentum tensor possessing dark energy with negative pressure and the energy equation of state is ρ+p=0. We have shown that a fluid has acceleration, rotation, shear-free, vanishing expansion, and rotation. In the case of a cosmic string cloud, we found that the tension density and particle density decrease as the fluid moves along the direction of the strings, then vanish at infinity. We shown that the exact conformal solution for a static plane symmetric model reduces to the well-known anti-De Sitter space-time. We obtained that the space-time under consideration admits a conformal vector field orthogonal to the 4-velocity vector and does not admits a vector parallel to the 4-velocity vector. Some physical and kinematic properties of the resulting models are also discussed.

Particle dynamics and Joule–Thomson expansion of phantom anti-de Sitter black hole stability and thermal fluctuations in massive gravity

Particle dynamics and Joule–Thomson expansion of phantom anti-de Sitter black hole stability and thermal fluctuations in massive gravity

Thermodynamic phase transition of Anti-de Sitter Reissner–Nordström black holes with exotic Einstein–Maxwell gravities

Thermodynamic phase transition of Anti-de Sitter Reissner–Nordström black holes with exotic Einstein–Maxwell gravities

Two optimization problems for the Loewner energy

A Jordan curve on the Riemann sphere can be encoded by its conformal welding, a circle homeomorphism. The Loewner energy measures how far a Jordan curve is away from being a circle, or equivalently, how far its welding homeomorphism is away from being a Möbius transformation. We consider two optimizing problems for the Loewner energy, one under the constraint for the curves to pass through n given points on the Riemann sphere, which is the conformal boundary of hyperbolic 3-space H3; the other under the constraint for n given points on the circle to be welded to another n given points of the circle. The latter problem can be viewed as optimizing positive curves on the boundary of AdS3 space passing through n prescribed points. We observe that the answers to the two problems exhibit interesting symmetries: optimizing the Jordan curve in ∂∞H3 gives rise to a welding homeomorphism that is the boundary of a pleated plane in AdS3, whereas optimizing the positive curve in ∂∞ AdS3 gives rise to a Jordan curve that is the boundary of a pleated plane in H3.

Pseudospectra of complex momentum modes

We initiate the study of stability and pseudospectra of complex momentum modes of asymptotically anti-de Sitter black holes. Similar to quasinormal modes, these can be defined as the poles of the holographic Green’s function, albeit for real frequency and complex momentum. Their pseudospectra are in stark contrast to the pseudospectra of quasinormal modes of AdS black holes. Contrary to the case of quasinormal mode pseudospectra, the resolvent is well-defined, and the numerical approximation shows fast convergence. At zero frequency, complex momentum modes are stable normal modes of a Hermitian operator. Even for large frequencies, they show only comparatively mild spectral instability. We also find that local potential perturbations cannot destabilize the lowest complex momentum mode.

Geodesics connecting endpoints of timelike interval in an asymptotically AdS spacetime

In the duality of 3-dimensional anti de-Sitter (AdS) spacetime and 2-dimensional conformal field theory (CFT), it was argued that the holographic entanglement entropy between two timelike separated events needs both timelike and spacelike geodesics. This paper studies the possibility of using smooth spacelike geodesics to connect two timelike separated events of boundary. We find that in a spherically symmetry Schwarzschild anti-de Sitter spacetime black hole, smooth spacelike geodesics can connect timelike-separated points by winding around the horizon multiple times. A similar result will also happen in a three-dimensional asymptotically AdS black hole that contains a photon ring in the bulk. Our result suggests that, if there is a photon ring, then the timelike entanglement entropy in the AdS3/CFT2 duality may not have an imaginary part. The result implies that the bulk photon ring may play an important role in understanding analytical behaviors of the entanglement spectrum for AdS3/CFT2 duality. Published by the American Physical Society 2025

Para-hyper-Kähler Geometry of the Deformation Space of Maximal Globally Hyperbolic Anti-de Sitter Three-Manifolds

In this paper we study the para-hyper-Kähler geometry of the deformation space of MGHC anti-de Sitter structures on Σ × R \Sigma \times \mathbb R , for Σ \Sigma a closed oriented surface. We show that a neutral pseudo-Riemannian metric and three symplectic structures coexist with an integrable complex structure and two para-complex structures, satisfying the relations of para-quaternionic numbers. We show that these structures are directly related to the geometry of MGHC manifolds, via the Mess homeomorphism, the parameterization of Krasnov-Schlenker by the induced metric on K K -surfaces, the identification with the cotangent bundle T ∗ T ( Σ ) T^*\mathcal T(\Sigma ) , and the circle action that arises from this identification. Finally, we study the relation to the natural para-complex geometry that the space inherits from being a component of the P S L ( 2 , B ) \mathbb {P}\mathrm {SL}(2,\mathbb {B}) -character variety, where B \mathbb {B} is the algebra of para-complex numbers, and the symplectic geometry deriving from Goldman symplectic form.

Matrix elements and characters of the discrete series (“massive”) unitary irreducible representations of Sp(4, ℝ)

This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp[Formula: see text] group. With an isomorphic relationship to the two-fold covering of [Formula: see text] ([Formula: see text][Formula: see text]), this group holds particular importance as the kinematical/relativity group within the framework of ([Formula: see text]-dimensional) anti-de Sitter spacetime.

TT¯ deformations from AdS2 to dS2

We revisit the formalism of TT¯ deformations for quantum theories that are holographically dual to two-dimensional dilaton-gravity theories with Dirichlet boundary conditions. To better understand the microscopics of de Sitter space, we focus on deformations for which the dual bulk geometry flows from Anti-de Sitter to de Sitter space. We explore two distinct ways to achieve this: either through so-called centaur geometries that interpolate between AdS2 and dS2, or by a spherical dimensional reduction of TT¯ + Λ2 theories that were proposed to give a microscopic interpretation of three-dimensional de Sitter entropy. We derive the microscopic energy spectrum, heat capacities, and deformed Cardy expressions for the thermodynamic entropy in the canonical and microcanonical ensembles for these two setups. In both setups a signature of the change from AdS to dS is that the heat capacity at a fixed deformation parameter of the boundary system changes sign, indicating the existence of a thermodynamically unstable de Sitter patch. Our findings provide important consistency conditions for holographic models of the dS2 static patch.

Rational Ruijsenaars-Schneider model with cosmological constant

The Ruijsenaars-Schneider models are integrable dynamical realizations of the Poincaré group in 1 + 1 dimensions, which reduce to the Calogero and Sutherland systems in the nonrelativistic limit. In this work, a possibility to construct a one-parameter deformation of the Ruijsenaars-Schneider models by uplifting the Poincaré algebra in 1 + 1 dimensions to the anti de Sitter algebra is studied. It is shown that amendments including a cosmological constant are feasible for the rational variant, while the hyperbolic and trigonometric systems are ruled out by our analysis. The issue of integrability of the deformed rational model is discussed in some detail. A complete proof of integrability remains a challenge.

Multitrace deformations and the nonlinear stability of anti–de Sitter space

We investigate the nonlinear stability of global anti–de Sitter space in the presence of multitrace deformations utilizing an Einstein-Klein-Gordon system with a top-down scalar potential. Our numerical simulations show that marginal and irrelevant deformations retain the nonlinear instability originally found by Bizoń and Rostworowski, while relevant deformations disrupt it. We show that the nonlinear impact of multitrace deformations is in one-to-one correspondence with how they affect the resonant character of the global anti–de Sitter normal mode eigenfrequency spectrum. Published by the American Physical Society 2025

Chiral transition and meson melting within improved holographic soft wall models

We describe the chiral transition for the quark condensate and the melting of scalar and vector mesons in two-flavor holographic quantum chromodynamics (holographic QCD). This is done by extending the improved holographic soft wall models proposed in Ballon-Bayona [] to finite temperature, by means of introducing an asymptotically anti–de Sitter black brane. We find that the chiral transition is second order in the chiral limit and a crossover for physical quark masses, as expected in two-flavor QCD. We investigate the melting of vector and scalar mesons in the deconfined plasma through the calculation of hadronic spectral functions. Fixing the model parameters by the meson spectrum at zero temperature, we find that the mesons melt at temperatures between 90 and 110 MeV and the chiral transition occurs around 129 MeV. We also provide a prediction for the hydrodynamic diffusion constant associated with a flavor current in the deconfined plasma. Published by the American Physical Society 2025

Bardeen-Dirac stars in Anti-de Sitter spacetime

In this paper, we construct a static spherical symmetric Bardeen-Dirac stars (BDSs) in the four-dimensional Anti-de Sitter (AdS) spacetime, which consists of the electromagnetic field and Dirac field coupled to gravity. We investigate the ADM mass, Noether charge and light rings of BDSs in AdS spacetime. In asymptotically Minkowski spacetime, the maximum frequency of BDSs is one. However, we observe that the maximum frequency of BDSs increases as the cosmological constant decreases in AdS spacetime. Additionally, BDSs can exhibit extreme behavior at low frequencies, refer to as Frozen Bardeen-Dirac stars (FBDSs) in AdS spacetime. FBDSs have a critical event horizon, where the metric function gtt is very close to zero. The matter is entirely encapsulated by this critical horizon, highly concentrated within it. When the magnetic charge is fixed, the FBDSs gradually disappear as the cosmological constant decreases.

Reduction of singularities in Fuchsian equations, and Heun equations for perturbations of Kerr–Newman–de Sitter and anti-de sitter spacetimes

For Fuchsian differential equations with N singularities at finite points we display two simply expressed conditions on coefficients which guarantee equivalence, under a certain inversion transformation, to a differential equation with N−1 singularities at finite points. For the radial and angular differential equations that govern perturbations of Kerr–Newman–de Sitter and anti-de Sitter spacetimes we find that these two conditions are satisfied identically for arbitrary values of all the parameters in the differential equations, including pole locations, with regular singularities and non-zero cosmological constant. From this we generalize the results of Suzuki, Tarasugi, and Umetsu, Prog. Theor. Phys. 100, 491 (1998) and find 128 Heun equations which are equivalent to the equations which govern the perturbations of the KN(A)dS spacetimes.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

Abstract We investigate the critical collapse of spherically symmetric scalar fields in asymptotically anti-de Sitter spacetime, focusing on two scenarios: real and complex scalar fields with potentials. By fine-tuning the amplitude of the initial scalar field under different cosmological constants, we find a linear relationship between the critical amplitude of the first collapse and the cosmological constant in both scenarios. Furthermore, we observe that the slope of this linear relationship varies linearly with the coupling strength.

Holographic Einstein Rings of AdS Black Holes in Horndeski Theory

Abstract By utilizing the AdS/CFT correspondence and wave optics techniques, we conducted an extensive study of the imaging properties of holographic Einstein rings in the context of Anti-de Sitter (AdS) black holes (BHs) in Horndeski theory. Our results indicate that the optical characteristics of these holographic Einstein rings are significantly influenced by the observer's position, the physical parameters of the BH, the nature of the wave source, and the configuration of the optical system. Specifically, when the observer is positioned at the north pole of the AdS boundary, the holographic image prominently displays a ring structure aligning with the BH's photon sphere. We thoroughly analyzed how various physical parameters---including the observation position, event horizon radius, temperature, and the parameter $\gamma$ in Horndeski theory---affect the holographic Einstein rings. These parameters play a crucial role in determining the rings' radius and brightness, with variations potentially causing the ring structures to deform or even transform into bright spots. Furthermore, our comparative analysis between wave optics and geometric optics reveals a strong agreement in predicting the positions and brightness of both the photon ring and the Einstein ring. This research offers new insights into the spacetime geometry of BHs in Horndeski theory and proposes a promising framework for exploring the gravitational duals of strongly coupled systems.