Holographic Principle Research Articles

CFT duals for black rings and black strings

Holographic dualities between certain gravitational theories in four and five spacetime dimensions and 2D conformal field theories (CFTs) have been proposed based on hidden conformal symmetry exhibited by the radial Klein-Gordon (KG) operator in a so-called near-region limit. In this paper, we examine hidden conformal symmetry of black rings and black strings solutions, thus demonstrating that the presence of hidden conformal symmetry is not linked to the separability of the KG-equation (or the existence of a Killing-Yano tensor). Further, we will argue that these classes of non-extremal black holes have a dual 2D CFT. New revised monodromy techniques are developed to encompass all the cases we consider.

BPS surface operators and calibrations

We present here a careful study of the holographic duals of BPS surface operators in the 6d theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form—a 3-form in whose pullback to the M2-brane world-volume is equal to the volume form. In all but one class, the appropriate forms are exact, so the action of the M2-brane is easily expressed in terms of boundary data, which is the geometry of the surface. Specifically, for surfaces of vanishing anomaly, it is proportional to the integral of the square of the extrinsic curvature. This can be extended to the case of surfaces with anomalies, by taking the ratio of two surfaces with the same anomaly. This gives a slew of new expectation values at large N in this theory. For one specific class of surface operators, which are Lagrangian submanifolds of , the structure is far richer and we find that the M2-branes are special Lagrangian submanifold of an appropriate six-dimensional almost Calabi-Yau submanifold of . This allows for an elegant treatment of many such examples.

Holographic duals of the mathcal{N} = 1* gauge theory

We use the long-wavelength effective theory of black branes (blackfold approach) to perturbatively construct holographic duals of the vacua of the mathcal{N} = 1* supersymmetric gauge theory. Employing the mechanism of Polchinski and Strassler, we consider wrapped black five-brane probes with D3-brane charge moving in the perturbative supergravity back-grounds corresponding to the high- and low-temperature phases of the gauge theory. Our approach recovers the results for the brane potentials and equilibrium configurations known in the literature in the extremal limit, while away from extremality we find metastable black D3-NS5 configurations with horizon topology ℝ3 × \U0001d54a2 × \U0001d54a3 in certain regimes of parameter space, which cloak potential brane singularities. We uncover novel features of the phase diagram of the mathcal{N} = 1* gauge theory in different ensembles and provide further evidence for the appearance of metastable states in holographic backgrounds dual to confining gauge theories.

Generalized quotients and holographic duals for 5d S-fold SCFTs

ℤn S-folds of 5d SCFTs, including TN, which lead to brane webs with E6,7,8 7-branes were discussed recently in [1, 2]. We generalize the construction to ‘fractional quotients’, which are based on ℤn actions linking multiple copies of the seed theory and lead to H0,1,2 7-branes. We provide the holographic duals for both classes. This expands the space of explicitly known Type IIB AdS6 solutions by incorporating F-theory 7-branes of type E6,7,8 and H0,1,2, extending previous constructions for O7-planes. We discuss observables including the free energies and link the results to matrix model descriptions.

Wilson loops for 5d and 3d conformal linear quivers

Within the electrostatic formulation of holographic duals to (balanced) conformal quivers in five and three dimensions, we study Wilson loops in antisymmetric representations. We derive general expressions for various quantities participating in the formalism (VEV of Wilson loops, representation, gauge-node) and apply these to examples, connecting some results present in the bibliography. In the case of three dimensional quivers, we present a relation between Wilson loops in an 'electric' and in the 'magnetic/mirror' descriptions. In a very detailed appendix, we relate the electrostatic and holomorphic description of the holographic duals to these SCFTS.

Monopoles and confinement in three dimensions from holography

We study the phase diagram of a confining three-dimensional mathcal{N} = 1 supersymmetric U(N) × U(N + M) theory with holographic dual corresponding to a known string theory solution. The theory possesses a global U(1) symmetry under which magnetic monopoles are charged. We introduce both temperature and an external magnetic field for monopoles and find that there are deconfinement phase transitions as any of the two is increased, supporting monopole condensation as the possible mechanism for confinement. We find that the transition as the magnetic field is increased is second order, providing the first example in holographic duals of a deconfinement transition which is not first order. We also uncover a rich structure in the phase diagram, with a triple point and a critical point where a line of first order transitions end.

Cauchy slice holography: a new AdS/CFT dictionary

We investigate a new approach to holography in asymptotically AdS spacetimes, in which time rather than space is the emergent dimension. By making a sufficiently large T2-deformation of a Euclidean CFT, we define a holographic theory that lives on Cauchy slices of the Lorentzian bulk. (More generally, for an arbitrary Hamiltonian constraint equation that closes, we show how to obtain it by an irrelevant deformation from a CFT with suitable anomalies.) The partition function of this theory defines a natural map between the bulk canonical quantum gravity theory Hilbert space, and the Hilbert space of the usual (undeformed) boundary CFT. We argue for the equivalence of the ADM and CFT Hamiltonians. We also explain how bulk unitarity emerges naturally, even though the boundary theory is not reflection-positive. This allows us to reformulate the holographic principle in the language of Wheeler-DeWitt canonical quantum gravity.Along the way, we outline a procedure for obtaining a bulk Hilbert space from the gravitational path integral with Dirichlet boundary conditions. Following previous conjectures, we postulate that this finite-cutoff gravitational path integral agrees with the T2-deformed theory living on an arbitrary boundary manifold — at least near the semiclassical regime. However, the T2-deformed theory may be easier to UV complete, in which case it would be natural to take it as the definition of nonperturbative quantum gravity.

Non-integrability of strings in AdS_{6}times S^{2}times Sigma background and its 5D holographic duals

In this manuscript we study Liouvillian non-integrability of strings in AdS_{6}times S^{2}times Sigma background. We consider soliton strings and look for simple solutions in order to reduce the equations to only one linear second order differential equation called Normal Variation Equation (NVE). We study truncations in eta and sigma variables showing their applicability or not to catch (non) integrability of models. With this technique we are able to study many recent cases considered in the literature: the abelian and non-abelian T-duals, the (p, q)-5-brane system, the T_{N}, +_{MN} theories and the {tilde{T}}_{N,P} and +_{P,N} quivers. We show that all of them are not integrable. Finally, we consider the general case at the boundary sigma =sigma _0 for large sigma _0 and show that we can get general conclusions about integrability. For example, beyond the above quivers, we show generically that long quivers are not integrable. In order to establish the results, we numerically study the string dynamical system seeking by chaotic behaviour. Such a characteristic gives one more piece of evidence for non-integrability of the background studied.

A proof for string three-point functions in AdS3

Correlation functions of the SL(2,ℝ)-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [1]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [2] based on the so-called SL(2,ℝ) series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the AdS3/CFT2 holographic duality at finite ’t Hooft coupling.

Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes

A deep dive on how the language of the holographic principle can simplify our understanding of quantum information processes (and vice versa), leading to a path toward exploring holographic theories of quantum gravity in tabletop experiments.

Thread/State correspondence: from bit threads to qubit threads

Starting from an interesting coincidence between the bit threads and SS (surface/state) correspondence, both of which are closely related to the holographic RT formula, we introduce a property of bit threads that has not been explicitly proposed before, which can be referred to as thread/state correspondence (see [50] for a brief pre-release version). Using this thread/state correspondence, we can construct the explicit expressions for the SS states corresponding to a set of bulk extremal surfaces in the SS correspondence, and nicely characterize their entanglement structure. Based on this understanding, we use the locking bit thread configurations to construct a holographic qubit threads model as a new toy model of the holographic principle, and show that it is closely related to the holographic tensor networks, the kinematic space, and the connectivity of spacetime.

Symmetry TFTs for 3d QFTs from M-theory

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their ’t Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold Y7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS4× Y7 holographic solution. In the holographic setting we first consider the 3d mathcal{N} = 6 ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d mathcal{N} = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y7 = Yp,k( mathbbm{CP} 2). The SymTFT encodes 0- and 1-form symmetries, as well as potential ’t Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT2s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS3/BCFT2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

Holographic dark energy through Kaniadakis entropy in non flat universe

By extending the standard holographic principle to a cosmological framework and combining the non-flat condition with the Kaniadakis entropy, we construct the non-flat Kaniadakis holographic dark energy (KHDE) model. The model employs Kaniadakis parameter K and a parameter c. Derivation of the differential equation for KHDE density parameter to describe the evolutionary behavior of the universe is obtained. Such a differential equation could explain both the open as well as closed universe models. The classification based on matter and dark energy (DE) dominated regimes show that the KHDE scenario may be used to specify the universe’s thermal history and that a quintom regime can be encountered. For both open and closed, we find the expressions for the deceleration parameter and the equation of state (EoS) parameter. Also, by varying the associated parameters, classical stability of the method is established. On considering the curvature to be positive, the universe favors the quintom behavior for substantially smaller values as opposed to the flat condition, when only quintessence is attained for such K values. Additionally, we see a similar behavior while considering the negative curvature for such K values. Therefore, adding a little bit of spatial geometry that isn’t flat to the KHDE enhances the phenomenology while maintaining K values at lower levels. To validate the model parameters, the most recent 30;H(z) dataset, in the redshift range 0.07 le z le 1.965 are utilized. In addition, the distance modulus from the current Union 2.1 data set of type SNIa are employed.

Top-Down Holography in an Asymptotically Flat Spacetime

We propose a holographic duality for a four dimensional Wess-Zumino-Witten model with target manifold SO(8), coupled to scalar-flat Kähler gravity on an asymptotically flat, four dimensional background known as the Burns metric. The holographic dual is a two dimensional chiral algebra built out of gauged β-γ systems with SO(8) flavor. We test the duality by matching two-point correlators of soft gluon currents with two-point gluon amplitudes, and their leading operator product expansion coefficients with collinear limits of three-point gluon amplitudes.

A Holographic Principle for Non-Relativistic Quantum Mechanics

The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and used to explain a selection of quantum phenomena. Introduced by Feynman, and used for modern quantum simulations, the isomorphism, when phrased in a field-theoretic way, has been shown to be the same as quantum density functional theory, the theorems of which guarantee equivalent predictions with non-relativistic quantum mechanics. If the Feynman dimension is considered to be real, there is a duality between classical threads in five dimensions and quantum particles in four dimensions. Using the 5D picture, intuitive explanations are given for quantum phenomena including the uncertainty principle, tunnelling, geometric phase, and interference effects. Advantages of the 5D picture are presented, which include fewer postulates, no measurement problem, and the need for only classical concepts in the higher dimensional space. Limitations of the approach such as the interpretation of entanglement and spin are discussed.

Categorical representation learning and RG flow operators for algorithmic classifiers

Following the earlier formalism of the categorical representation learning, we discuss the construction of the ‘RG-flow-based categorifier’. Borrowing ideas from the theory of renormalization group (RG) flows in quantum field theory, holographic duality, and hyperbolic geometry and combining them with neural ordinary differential equation techniques, we construct a new algorithmic natural language processing architecture, called the RG-flow categorifier or for short the RG categorifier, which is capable of data classification and generation in all layers. We apply our algorithmic platform to biomedical data sets and show its performance in the field of sequence-to-function mapping. In particular, we apply the RG categorifier to particular genomic sequences of flu viruses and show how our technology is capable of extracting the information from given genomic sequences, finding their hidden symmetries and dominant features, classifying them, and using the trained data to make a stochastic prediction of new plausible generated sequences associated with a new set of viruses which could avoid the human immune system.

D4-branes wrapped on four-dimensional orbifolds through consistent truncation

We construct a consistent truncation of six-dimensional matter coupled F(4) gauged supergravity on a cornucopia of two-dimensional surfaces including a spindle, disc, domain wall and other novel backgrounds to four-dimensional minimal gauged supergravity. Using our consistent truncation we uplift known AdS2× Σ1 solutions giving rise to four-dimensional orbifold solutions, AdS2× Σ1 ⋉ Σ2. We further uplift our solutions to massive type IIA supergravity by constructing the full uplift formulae for six-dimensional U(1)2-gauged supergravity including all fields and arbitrary Romans mass and gauge coupling. The solutions we construct are naturally interpreted as the near-horizon geometries of asymptotically AdS6 black holes with a four-dimensional orbifold horizon. Alternatively, one may view them as the holographic duals of superconformal quantum mechanical theories constructed by compactifying five-dimensional USp(2N) theory living on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step to identifying these quantum mechanical theories we compute the Bekenstein-Hawking entropy holographically.

THE CONNECTION BETWEEN SCHRÖDINGER EQUATION AND QUANTUM FIELD THEORY

The purpose of this research review is to examine the connection between the Schrödinger equation and quantum field theory. The method used in this review is a literature review of existing research on the topic. The results of the review indicate that the Schrödinger equation, which is a fundamental equation in quantum mechanics, can be derived from the principles of quantum field theory. This connection highlights the underlying unity of the two theories and helps to further our understanding of the behavior of subatomic particles. Additionally, it has been found that the Schrödinger equation is useful in describing the behavior of systems with a small number of particles, while quantum field theory is more appropriate for systems with a large number of particles. Research in this area has led to the development of new methods for solving the equation, such as the path integral approach, which provides a powerful tool for studying quantum systems with a large number of degrees of freedom. Additionally, the Schrödinger equation has led to the discovery of new symmetries and conservation laws, such as the AdS/CFT correspondence, which connects quantum field theory in anti-de Sitter space with a conformal field theory on the boundary of that space. Theoretical frameworks such as quantum field theory in curved spacetime and the holographic principle have also been developed to unify quantum mechanics and general relativity, and to understand the thermodynamic behavior of quantum systems and their behavior in extreme conditions. The study of quantum systems in non-equilibrium conditions is an active area of research and continues to yield new insights and discoveries. Overall, the research reviewed in this study suggests that the Schrödinger equation and quantum field theory are closely related, and that a deeper understanding of one can lead to a deeper understanding of the other. KEYWORDS: Schrödinger equation, quantum field theory, general relativity, quantum systems

Holographic energy density, dark energy sound speed, and tensions in cosmological parameters: H0 and S8

Interesting discrepancies in cosmological parameters are challenging the success of the ΛCDM model. Direct measurements of the Hubble constant H 0 using Cepheid variables and supernovae turn out to be higher than inferred from the Cosmic Microwave Background (CMB). Weak galaxy lensing surveys consistently report values of the strength of matter clustering σ 8 lower than values derived from the CMB in the context of ΛCDM. In this paper we address these discrepancies in cosmological parameters by considering Dark Energy (DE) as a fluid with evolving equation of state w de(z), constant sound speed squared ĉ s 2, and vanishing anisotropic stress σ. Our w de(z) is derived from the Holographic Principle and can consecutively exhibit radiation-like, matter-like, and DE-like behaviour, thus affecting the sound horizon and the comoving angular diameter distance, hence H 0. Here we show DE sound speed plays a part in the matter clustering behaviour through its effect on the evolution of the gravitational potential. We compute cosmological constraints using several data set combinations including primary CMB, CMB lensing, redshift-space-distortions, local distance-ladder, supernovae, and baryon acoustic oscillations. In our analysis we marginalise over ĉ s 2 and find ĉ s 2 = 1 is excluded at ≳ 3σ. For our baseline result including the whole data set we found H 0 and σ 8 in good agreement (within ≈ 2σ) with low redshift probes. Our constraint for the baryon energy density ω b is however in ≈ 3σ tension with BBN constraints. We conclude evolving DE also having non-standard clustering properties [e.g., ĉ s 2(z,k)] might be relevant for the solution of current discrepancies in cosmological parameters.