In this paper, we study excited states in anti–de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual conformal field theory states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (“hard wall”), thereby creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory with the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in the temporal dynamics are closest to those of the Gaussian symplectic ensemble. Finally, we extend the analysis to the compact Bañados-Teitelboim-Zanelli black hole and to its hard-wall deformation, where we find qualitatively similar trends.

A bstract The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

ABSTRACT Traditional remote sensing image fusion techniques often suffer from spectral distortion or spatial information loss. Moreover, the performance quality of deep learning-based methods is inconsistent, and they necessitate separate training processes, thereby constraining their practical applicability. A network framework for fusing different satellite remote sensing images is developed to address this issue. The framework structure mainly includes two stages. In the first stage, the research utilises Squeeze-and-Excitation Network (SEN) technology to significantly improve and optimise the geometric details of the image, enhancing the overall visual effect of the image. In the second stage, different Spectral Attention Networks (SAN) are studied to adjust the chromatic data in the SEN results. In both simulated and real data testing, the research method performs excellently on the GeoEye-1, WorldView-4, and Quick Bird datasets, outperforming the comparison models. In GeoEye-1, its spectral distortion index and no reference quality index perform the best, and its chromatic data are superior. In WorldView-4, the DS metric is the best, with an improvement of over 10% and rich geometric details. The results indicate that the research method has high image fusion quality and significant advantages in chromatic data and geometric details.

Presently integrability turned out to be the key property in the study of duality between superconformal gauge theories and strings in anti-de Sitter superspaces. Complexity of the study of integrable structure in string theory is caused by complicated dependence of background fields of the Type II supergravity multiplets, with which strings interact, on the superspace coordinates. This explains an interest to study of limiting cases, in which superstring equations simplify. In the present work, we considered the limiting case of zero tension corresponding to null string. The representation in the form of the Lax equation of null-string equations in (anti-)de Sitter space realized as a coset manifold is obtained. Proposed is twistor interpretation of the Lagrangian of (null) string in anti-de Sitter space expressed in terms of group variables.

This research examines the thermodynamic characteristics and trajectories of particles surrounding a charged black hole within the framework of [Formula: see text] gravity combined with nonlinear electrodynamics. It evaluates how the parameters [Formula: see text], [Formula: see text], and [Formula: see text] introduce gravitational and electromagnetic adjustments beyond the scope of general relativity. The paper concentrates on the lapse function [Formula: see text], demonstrating that the count of black hole horizons may increase to three or four, contingent on whether [Formula: see text] is positive or negative. We assess thermodynamic aspects including the mass function, Hawking temperature, and thermal stability. A positive [Formula: see text] creates an environment akin to de Sitter space, which reduces temperature and phase transitions, while a negative [Formula: see text] (similar to AdS) enhances confinement and promotes Hawking-Page-type transitions. The coupling parameter [Formula: see text] intensifies the effective cosmological term, leading to a decrease in [Formula: see text] and overall stability. Additionally, we investigate the effective potential, angular momentum, energy, and stability of the circular orbit of a time-like particle. This study reveals alternating stability zones for circular orbits and demonstrates how alterations in gravity and nonlinear electrodynamics modify the spacetime curvature encountered by particles in orbit.

A bstract We investigate a new definition of holographic entanglement entropy in the framework of static patch holography for de Sitter space. Using the replica trick and twist operator formalism, we derive an entropy functional in dS 3 expressed through de Sitter Green’s functions. Since the naive Ryu-Takayanagi prescription in de Sitter spacetime fails to satisfy strong subadditivity, we demand that our proposed formula be consistent with the fundamental entropic inequalities. The resulting conditions place nontrivial constraints on the undetermined parameter space of static patch holography. Our results demonstrate that entanglement inequalities provide a sharp diagnostic for candidate definitions of entanglement entropy in de Sitter holography and offer quantitative evidence in support of static patch holography as a consistent framework.

Abstract We investigate the entanglement content of a free, light scalar field theory in the Bunch-Davies vacuum within the cosmological patch of de Sitter spacetime, focusing on how entanglement varies with the Hubble rate H. We find that the entanglement between any spacelike-separated pair of field modes localized in finite regions decreases as H increases. This occurs despite the fact that correlations between such local modes increase with H. Consequently, these correlations do not contribute to entanglement. Our analysis elucidates how entanglement is distributed in de Sitter space and demonstrates that localized field modes at the end of inflation are less entangled than they would be in the Minkowski vacuum of flat spacetime.

The cosmological constant (CC, Λ) problem stands as one of the most profound puzzles in the theory of gravity, representing a remarkable discrepancy of about 120 orders of magnitude between the observed value of dark energy and its natural expectation from quantum field theory. This paper synthesizes two innovative paradigms—holographic naturalness (HN) and pre-geometric gravity (PGG)—to propose a unified and natural resolution to the problem. The HN framework posits that the stability of the CC is not a matter of radiative corrections but rather of quantum information and entropy. The large entropy SdS∼MP2/Λ of the de Sitter (dS) vacuum (with MP being the Planck mass) acts as an entropic barrier, exponentially suppressing any quantum transitions that would otherwise destabilize the vacuum. This explains why the universe remains in a state with high entropy and relatively low CC. We then embed this principle within a pre-geometric theory of gravity, where the spacetime geometry and the Einstein–Hilbert action are not fundamental, but emerge dynamically from the spontaneous symmetry breaking of a larger gauge group, SO(1,4)→SO(1,3), driven by a Higgs-like field ϕA. In this mechanism, both MP and Λ are generated from more fundamental parameters. Crucially, we establish a direct correspondence between the vacuum expectation value (VEV) v of the pre-geometric Higgs field and the de Sitter entropy: SdS∼v (or v3). Thus, the field responsible for generating spacetime itself also encodes its information content. The smallness of Λ is therefore a direct consequence of the largeness of the entropy SdS, which is itself a manifestation of a large Higgs VEV v. The CC is stable for the same reason a large-entropy state is stable: the decay of such state is exponentially suppressed. Our study shows that new semi-classical quantum gravity effects dynamically generate particles we call “hairons”, whose mass is tied to the CC. These particles interact with Standard Model matter and can form a cold condensate. The instability of the dS space, driven by the time evolution of a quantum condensate, points at a dynamical origin for dark energy. This paper provides a comprehensive framework where the emergence of geometry, the hierarchy of scales and the quantum-information structure of spacetime are inextricably linked, thereby providing a novel and compelling path toward solving the CC problem.

The Klein-Gordon and Dirac equation for a massive charged field in a uniform electric field has a symmetry of two-dimensional global de Sitter (dS) and anti–de Sitter (AdS) space. In the in-out formalism the mean numbers of spinors (spin- 1 / 2 fermions) and scalars (spin-0 bosons) spontaneously produced by the uniform electric field are exactly found from the Bogoliubov relations both in the global and planar coordinates of (A) dS 2 space. We show that the uniform electric field enhances the production of charged spinor and scalar pairs in the planar and global dS space while the AdS space reduces the pair production in which weak electric fields below the Breitenlohner-Freedman bound prohibits pair production. The leading Boltzmann factor in dS space can be written as the Gibbons-Hawking radiation or Schwinger effect enhanced by e-folding factors less than one that give the QED effect or the curvature effect. We observe that dS 2 and AdS 2 spaces are connected by QED, such as a reciprocal relation between the mean number of spinors and scalars provided that the spacetime curvature is analytically continued. The leading behavior of the mean numbers for spinors and scalars is explained as a residue sum of contour integrals of the frequency or momentum in the phase-integral formulation.

A bstract An important insight from the study of AdS/CFT is that bulk locality can be derived from crossing symmetry of the boundary CFT. In this paper, we take the first steps in extending this statement to de Sitter background by demonstrating how to reconstruct a conformally coupled scalar effective field theory (EFT) with higher derivative interactions in four-dimensional de Sitter space from its in-in correlators. The latter can be computed from a certain EFT in Euclidean Anti-de Sitter space involving two scalar fields, which we derive from crossing symmetry of boundary correlators along with two novel constraints arising from unmixing anomalous dimensions of degenerate operators and equating them in different OPE channels. To facilitate the analysis, we work in Mellin space and apply dispersion relations to extract anomalous dimensions more efficiently.

We investigate elliptical Wilson loops in N = 4 Super Yang–Mills theory at weak and strong coupling for small values of the eccentricity. We obtain analytical results for the vacuum expectation value of the Wilson loop in the form of a series in the eccentricity parameter. At weak coupling, we use perturbation theory in N = 4 Super Yang–Mills. At strong coupling, we use the AdS/CFT correspondence, which maps the Wilson loop to the minimal-area world sheet of an open string in anti–de Sitter (AdS) space. We present a novel perturbative method to solve the Nambu–Goto equations allowing us to describe the minimal surface in terms of a coordinate parametrization in Euclidean AdS 3 . Our results for the regularized area agree with those obtained by Dekel [.] based on the Polyakov action.

Soft unification of exceptional effective field theories in de Sitter space

De Sitter entropy: On-shell versus off-shell

A bstract We consider soft graviton scattering for a theory where Einstein’s gravity is minimally coupled to a scalar field in the presence of a cosmological constant, i.e. in a background de Sitter space. Employing a perturbative expansion in a small cosmological constant, we compute leading, subleading and sub-subleading corrections to Weinberg’s soft graviton amplitude for the tree-level scatterings in the static patch of de Sitter space. We observe similar universal features of the soft graviton amplitude as found in JHEP 10 (2023) 055 for the soft photons.

Abstract We discuss and formalize topological means by which the initial singularity might be mollified, at the level of the spacetime manifold’s structure, in classical cosmological models of a homogeneous expanding Universe. One construction, dubbed a ‘reflective’ topological big bang , generalizes Schrödinger’s elliptic de Sitter space and is built to be compatible with the standard Friedmann–Lemaitre–Robertson–Walker picture of the large-scale Universe, only minimally modifying it via some nontrivial topology at an earliest ‘moment’ in the Universe’s history. We establish a mathematical characterization of the admissible topological structures of reflective topological big bangs, and we discuss implications for a standard concern in cosmology, the horizon problem. We present a nonreflective example that we have christened the Itty-Bitty Blender spacetime: this spacetime and its universal cover, the Eternal Trumpet spacetime, exhibit interesting potential structures of spacetimes avoiding the Hawking and Penrose singularity theorems. While these toy models provide a proof-of-concept picture, several questions remain regarding the capacity to realize these structures under physical energy conditions.

A bstract In the limit of infinite radius de Sitter space becomes locally flat and the static patch tends to Rindler space. A holographic description of the static patch must result in a holographic description of some flat space theory, expressed in Rindler coordinates. Given such a holographic theory how does one decode the hologram and determine the bulk flat space theory, its particle spectrum, forces, and bulk quantum fields? In this paper we will answer this question for a particular case: DSSYK at infinite temperature and show that the bulk theory is a strongly coupled version of the ’t Hooft model, i.e., (1+1)-dimensional QCD, with a single quark flavor. It may also be thought of as an open string theory with mesons lying on a single Regge trajectory.

Abstract We combine the well-known Beltrami–Klein model of non-Euclidean geometry on a two-dimensional disk, where the geodesics are the chords of the disk, with the two—dimensional de Sitter space. The geometry of the de Sitter space is defined on the complement of the Beltrami–Klein disk in the plane, with the de Sitter metric being the unique Lorentzian Einstein metric whose light cones form cones tangent to the disk in this complement. This leads to a Beltrami–de Sitter model on the plane R 2 , which is endowed with the Riemannian Beltrami metric on the disk and the Lorentzian de Sitter metric outside the disk in R 2 . We explore the relevance of this model for Penrose’s conformal cyclic cosmology, first in the two-dimensional setting and subsequently in higher dimensions, including the physically significant case of four dimensions. In this context, we define a Radon-like transform between the de Sitter and Beltrami spaces, facilitating the purely geometric transformation of physical fields from the Lorentzian de Sitter space to the Riemannian Beltrami space. In the two –, and three-dimensional cases, we also uncover a hidden G 2 symmetry associated with the de Sitter spaces in these dimensions, which is related to a certain vector distribution naturally defined by the geometry of the model. We suggest the potential for discovering similar hidden symmetries in the n -dimensional Beltrami–de Sitter model.

We discover a surprising relationship between exceptional effective field theories (EFTs) in de Sitter space and a notion of (GEC) of an S matrix defined in an extended Poincaré patch of four-dimensional de Sitter. By demanding that such an S matrix has support only when the total energies of in and out states are equal, we constrain the coupling constants in theories of self-interacting scalars living in the exceptional series of de Sitter representations. We rediscover the theories of Dirac-Born-Infeld (DBI) and special Galileon, and when increasing the conformal dimension, we find evidence for new exceptional theories where the four-point scalar self-interactions are uniquely fixed in terms of a single coupling constant. We conjecture that for each integer conformal dimension Δ ≥ 4 , there is at least one exceptional EFT that can be entirely fixed by GEC.

Abstract The application of nonlinear electrodynamics at high energy scales has led to a variety of interesting phenomena in recent years, particularly within the context of non-singular spacetime geometries. Additionally, it is postulated that gravity near the Planck scale is governed by a minimal cut-off length, which acts as a renormalization scale against ultraviolet pathologies. Within this framework, we combine both concepts by introducing modifications to the electric and matter sectors of a black hole as its size approaches this minimal length. The result is an electrically charged black hole that is free from ultraviolet divergences and recovers the Maxwell limit at classical scales. We further explore the geometric and thermodynamic properties of the resulting solution within a cosmological anti-de Sitter background, revealing a chemical analogy with that of a Van der Waals fluid. Subsequently, we examine the charged black hole in de Sitter space and construct four corresponding gravitational instantons. We then study their cosmological quantum production using the formalism of the pair creation rate within the context of the no-boundary proposal.

The spectral form factor is believed to exhibit a special type of behavior called “dip-ramp-plateau” in chaotic quantum systems that originates from random matrix theory. This suggests that the shape of the spectral form factor could serve as an indicator of chaos in various quantum systems. It has been shown recently that the dip-ramp-plateau structure appears in the spectral form factor when the normal modes of a massless scalar field theory in the brick-wall model of the Bañados-Teitelboim-Zanelli black hole are treated as eigenvalues of a quantum Hamiltonian. At the same time, the level spacing distribution of these normal modes differs from that associated with random matrix theory ensembles if no averaging over randomly distributed boundary conditions is taken into account. In this paper, we extend the results for BTZ background to the case of a nonzero mass of the field, study the generalized spectral form factor, and consider the same context for another nontrivial background—de Sitter space. We compare the generalized spectral form factor for simple integrable quantum systems and for backgrounds with a horizon to the behavior predicted by random matrix theory. As a result, we confirm that BTZ and de Sitter brick-wall models without averaging exhibit the dip-ramp-plateau structure of the spectral form factor but differ in the structure of the three-level generalized spectral form factor from the one predicted by random matrix theory.