Holographic Principle Research Articles

A new observable for holographic cosmology

The double-cone geometry is a saddle of the gravitational path integral, which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole, but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. Here, we consider generalizations of the double-cone geometry which include the Lorentzian cosmology that sits between the event horizon and the black hole singularity. We analyze this in two and three dimensions, where the cosmology has compact spatial sections and big bang/crunch singularities. These singularities are regulated in the same way by slightly complexifying the metric. We show that this is possible while satisfying the Kontsevich-Segal criterion, implying that these geometries can be interpreted as perturbatively stable saddle points in general relativity. This procedure leads to a novel description of the cosmology in terms of standard observables in the dual boundary CFT. In three dimensions, the cosmological solution gives a new contribution to the two-point function of the density of states in the boundary CFT. Unlike the usual double cone, it describes correlations between black hole microstates with different masses, and in a limit describes correlations between the statistics of heavy states and states near the BTZ threshold.

Pseudospectra of quasinormal modes and holography

The holographic duality (also known as AdS/CFT correspondence or gauge/gravity duality) postulates that strongly coupled quantum field theories can be described in a dual way in asymptotically anti-de Sitter space. One of the cornerstones of this duality is the description of thermal states as black holes with asymptotically anti-de Sitter boundary conditions. This idea has led to valuable insights into fields such as transport theory and relativistic hydrodynamics. In this context, the quasinormal modes of such black holes play a decisive role, and therefore their stability properties are of utmost interest for the holographic duality. We review recent results using the method of pseudospectra.

Probing barrow entropy models with future event horizon as IR cutoff

We develop formulations for barrow holographic dark energy (BHDE) in both non-interacting and interacting scenarios within a cosmological framework, applying the conventional holographic principle. Model parameter constraints are determined through the Markov Chain Monte Carlo (MCMC) method, utilizing different datasets. The investigation excavates into the models' kinematic behavior, exploring the transition from deceleration to acceleration and tracking the evolution of the equation of state parameters. Further, these models can pretend the evolution of dark energy and matter in the Universe. Additionally, a thermodynamic analysis employing future event horizons is conducted, confirming the validation of the generalized second law of thermodynamics. The resultant of the BHDE models strongly suggests that the Universe is presently experiencing an accelerated phase attributed to dark energy.

Advanced directional beam control via holographic acoustic metasurfaces for multibeam scanning

Acoustic multi-beam leaky-wave antennas, designed with holographic metasurfaces, have great potential for beamforming by achieving directional beam control. We propose a planar holographic metasurface for beam steering using multi-beam acoustic radiation serving as high-gain acoustic leaky wave antennas. Based on the principle of holography, we designed a metasurface that adjusts its admittance in a sinusoidal pattern. This surface consists of periodic cylindrical holes with varying depth profiles. A monopole point source is positioned in the middle of the patterned surface, which generates surface waves on the modulated surface and emits acoustic leaky-wave radiation in the desired directions. The holographic admittance surface is designed to radiate an acoustic beam at a frequency of 20 kHz. Additionally, the concept was extended to generate multi-beam scanning for forward leaky-wave radiation in the holographic process. In this research, we employed 3D additive manufacturing to create acoustic holograms, manipulating surface admittance variation at a resolution smaller than the wavelength. The experimental measurements aligned well with both the theoretical and numerical analysis findings, affirming the effectiveness of the proposed technique. The methodology exhibits broad applicability across various domains, including sonar, ultrasound imaging, waveform manipulation, and acoustic communication.

On AdS3/ICFT2 with a dynamical scalar field located on the brane

We exploit the holographic duality to study the system of a one-dimensional interface contacting two semi-infinite two-dimensional CFTs. Central to our investigation is the introduction of a dynamical scalar field located on the bulk interface brane which breaks the scaling symmetry of the dual interface field theory, along with its consequential backreaction on the system. We define an interface entropy from holographic entanglement entropy, to construct a g-function. At zero temperature we construct several illustrative examples and consistently observe that the g-theorem is always satisfied. These examples also reveal distinct features of the interface entropy that are intricately linked to the scalar potential profiles. At finite temperature we find that the dynamical scalar field enables the bulk theory to have new configurations which would be infeasible solely with a tension term on the interface brane.

Quasinormal modes and universality of the Penrose limit of black hole photon rings

We study the physics of photon rings in a wide range of axisymmetric black holes admitting a separable Hamilton-Jacobi equation for the geodesics. Utilizing the Killing-Yano tensor, we derive the Penrose limit of the black holes, which describes the physics near the photon ring. The obtained plane wave geometry is directly linked to the frequency matrix of the massless wave equation, as well as the instabilities and Lyapunov exponents of the null geodesics. Consequently, the Lyapunov exponents and frequencies of the photon geodesics, along with the quasinormal modes, can be all extracted from a Hamiltonian in the Penrose limit plane wave metric. Additionally, we explore potential bounds on the Lyapunov exponent, the orbital and precession frequencies, in connection with the corresponding inverted harmonic oscillators and we discuss the possibility of photon rings serving as effective holographic horizons in a holographic duality framework for astrophysical black holes. Our formalism is applicable to spacetimes encompassing various types of black holes, including stationary ones like Kerr, Kerr-Newman, as well as static black holes such as Schwarzschild, Reissner-Nordström, among others.

Multifunctional multifocal lens for simultaneous edge and polarisation imaging

ABSTRACT The method of inserting ultrathin devices in the Fourier plane of the 4F imaging system can achieve multifunctional imaging. However, such a method generally requires precise alignment in the system, which also makes the system more complex. Here, we present an imaging system that incorporates a multifocal Pancharatnam–Berry (PB) phase liquid crystal (LC) lens capable of achieving simultaneous edge and polarisation imaging. Without placing optical elements in the Fourier plane of the 4F system, the proposed imaging system replace a refracted lens in 4F system by multifocal LC lens, which integrates edge and polarisation imaging modes. The phase distribution of multifocal lens is obtained through manipulating the positions and polarisation states of four foci with holographic principles. Furthermore, the imaging system based on the proposed multifocal lens has been shown to be effective in simultaneously achieving polarisation and edge imaging with broadband characteristics. The proposed optical system effectively reduces the complexity of the imaging system, which is expected to be applied in the fields of biomedical imaging, optical interconnection and microscopic imaging.

Holographic RG flows in a 3D gauged supergravity at finite temperature

In this paper, we consider finite-temperature holographic renormalization group (RG) flows in D=3 N=(2,0) gauged truncated supergravity coupled to a sigma model with a hyperbolic target space. In the context of the holographic duality, fixed points (CFTs) at finite temperature are described by anti–de Sitter (AdS) black holes. We come from the gravity equations of motion to a 3D autonomous dynamical system, which critical points can be related to fixed points of dual field theories. Near-horizon black hole solutions correspond to infinite points of this system. We use Poincaré transformations to project the system on R3 into the 3D unit cylinder such that the infinite points are mapped onto the boundary of the cylinder. We explore numerically the space of solutions. We show that the exact RG flow at zero temperature is the separatrix for asymptotically AdS black hole solutions if the potential has one extremum, while for the potential with three extrema the separatrices are RG flows between AdS fixed points. We find near-horizon analytical solutions for asymptotically AdS black holes using the dynamical equations. We also present a method for constructing full analytical solutions. Published by the American Physical Society 2024

Capacity of entanglement and volume law

We investigate various aspects of capacity of entanglement in certain setups whose entanglement entropy becomes extensive and obeys a volume law. In particular, considering geometric decomposition of the Hilbert space, we study this measure both in the vacuum state of a family of non-local scalar theories and also in the squeezed states of a local scalar theory. We also evaluate field space capacity of entanglement between interacting scalar field theories. We present both analytical and numerical evidences for the volume law scaling of this quantity in different setups and discuss how these results are consistent with the behavior of other entanglement measures including Renyi entropies. Our study reveals some generic properties of the capacity of entanglement and the corresponding reduced density matrix in the specific regimes of the parameter space. Finally, by comparing entanglement entropy and capacity of entanglement, we discuss some implications of our results on the existence of consistent holographic duals for the models in question.

Fuzzy Sets and the Holographic Principle: Uncertainty in Black Hole Physics

Black hole physics, with its profound implications for gravity, spacetime, and the universe'sfundamental structure, remains a challenging field riddled with uncertainties. This study explores theintegration of fuzzy set theory and the holographic principle to address the inherent imprecision in blackhole parameter measurements and advance our understanding of these enigmatic cosmic entities.Hypothetical data sets, characterized by fuzzy set representations of uncertainties, are subjected tofuzzy set-based analysis. Fuzzy entropy calculations reveal the degree of imprecision, while fuzzyclustering suggests the potential existence of distinct black hole classes. This interdisciplinary approachprovides new theoretical insights, challenges existing models, and emphasizes the need for furtherresearch to validate and refine these concepts.

Temperatures of AdS2 black holes and holography revisited

In a dilaton gravity model, we revisit the calculation of the temperature of an evaporating black hole that is initially formed by a shock wave, taking into account the quantum backreaction. Based on the holographic principle, along with the assumption of a boundary equation of motion, we show that the black hole energy is maintained for a while during the early stage of evaporation. Gradually, it decreases as time goes on and eventually vanishes. Thus, the Stefan–Boltzmann law tells us that the black hole temperature, defined by the emission rate of the black hole energy, starts from zero temperature and reaches a maximum value at a critical time, and finally vanishes. It is also shown that the maximum temperature of the evaporating black hole never exceeds the Hawking temperature of the eternal AdS2 black hole. We discuss physical implications of the initial zero temperature of the evaporating black hole.

Thermodynamics and dynamics of coupled complex SYK models.

It has been known that the large-q complex SYK model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-q complex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-q limit at low temperatures, adhering to the Maldacena-Shenker-Stanford bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the ``very" low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be be taken to make the connection robust.

Capacity of entanglement for scalar fields in squeezed states

We study various aspects of capacity of entanglement in the squeezed states of a scalar field theory. This quantity is a quantum informational counterpart of heat capacity and characterizes the width of the eigenvalue spectrum of the reduced density matrix. In particular, we carefully examine the dependence of capacity of entanglement and its universal terms on the squeezing parameter in the specific regimes of the parameter space. Remarkably, we find that the capacity of entanglement obeys a volume law in the large squeezing limit. We discuss how these results are consistent with the behavior of other entanglement measures including entanglement and Renyi entropies. We also comment on the existence of consistent holographic duals for a family of Gaussian states with generic squeezing parameter based on the ratio of entanglement entropy and the capacity of entanglement. Published by the American Physical Society 2024

Holographic phenomenology via overlapping degrees of freedom

Abstract The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define $N \gg n$ Pauli algebras that are nearly anti-commuting (but not quite) and which can be thought of as ``overlapping degrees of freedom". We propose to model the phenomenology of holographic theories by allowing field-theory modes to be overlapping, and derive potential observational consequences. In particular, we build a Fermionic quantum field whose effective degrees of freedom approximately obey area scaling and satisfy a cosmic Bekenstein bound, and compare predictions of that model to cosmic neutrino observations. Our implementation of holography implies a finite lifetime of plane waves, which depends on the overall UV cutoff of the theory. To allow for neutrino flux from blazar TXS 0506+056 to be observable, our model needs to have a cutoff $k_{\mathrm{UV}} \lesssim 500\, k_{\mathrm{LHC}}\,$. This is broadly consistent with current bounds on the energy spectrum of cosmic neutrinos from IceCube, but high energy neutrinos are a potential challenge for our model of holography. We motivate our construction via quantum mereology, \ie using the idea that EFT degrees of freedom should emerge from an abstract theory of quantum gravity by finding quasi-classical Hilbert space decompositions. We also discuss how to extend the framework to Bosons. Finally, using results from random matrix theory we derive an analytical understanding of the energy spectrum of our theory.\ \ The numerical tools used in this work are publicly available within the \verb|GPUniverse| package, \url{https://github.com/OliverFHD/GPUniverse}~.

Holographic turbulence from a random gravitational potential

We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid placed in a stochastic gravitational potential. We demonstrate that the dynamics of the fluid can be obtained using a dual holographic description realized by an asymptotically Anti-de Sitter black brane driven by a random boundary metric. Using the holographic duality we study the energy power spectrum of a fluid with an inverse energy cascade and show that it is compatible with that of a compressible fluid flow. We calculate the local energy dissipation and the local fluid velocity distribution which provide other measures of the holographic fluid turbulence.

Duality origami: Emergent ensemble symmetries in holography and Swampland

We discuss the interrelations between several ideas in quantum gravity – holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic forms and their holographic duals. We establish the emergence of global symmetries and discuss their consistency with conjectures forbidding such symmetries. We also discuss how the spectral decomposition of Narain partition functions suggests a natural embedding of ensemble averaging within the low-energy limit of certain string compactifications, which in turn allows a connection with the Swampland program.

Microstates of Accelerating and Supersymmetric AdS_{4} Black Holes from the Spindle Index.

We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in AdS_{4}. This is achieved by analyzing the large-N limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.

G Theorem from Strong Subadditivity.

We show that strong subadditivity provides a simple derivation of the g theorem for the boundary renormalization group flow in two-dimensional conformal field theories. We work out its holographic interpretation and also give a derivation of the g theorem for the case of an interface in two-dimensional conformal field theories. We also geometrically confirm strong subadditivity for holographic duals of conformal field theories on manifolds with boundaries.

The Holographic Principle Comes from Finiteness of the Universe's Geometry.

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe's surface.

Cosmological singularities, holographic complexity and entanglement

We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with AdS, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.