Anti-de Sitter/conformal Field Theory Research Articles

Engineering holography with stabilizer graph codes

The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the experimental realization of such holographic codes now within reach. Formulating the hyperbolic pentagon code in terms of a stabilizer graph code, we give gate sequences that are tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code, before focusing on a small instance of the holographic code on twelve qubits. Our approach allows to verify holographic properties by partial decoding operations, recovering bulk degrees of freedom from their nearby boundary.

Cosmological constant as quantum error correction from generalized gauge invariance in double field theory

The holographic principle and its realization as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence leads to the existence of the so-called precursor operators. These are boundary operators that carry nonlocal information regarding events occurring deep inside the bulk and which cannot be causally connected to the boundary. Such nonlocal operators can distinguish nonvacuum-like excitations within the bulk that cannot be observed by any local gauge invariant operators in the boundary. The boundary precursors are expected to become increasingly nonlocal the further the bulk process is from the boundary. Such phenomena are expected to be related to the extended nature of the strings. Standard gauge invariance in the boundary theory equates to quantum error correction which furthermore establishes localization of bulk information. I show that when double field theory quantum error correction prescriptions are considered in the bulk, gauge invariance in the boundary manifests residual effects associated to stringy winding modes. Also, an effect of double field theory quantum error correction is the appearance of positive cosmological constant. The emergence of space–time from the entanglement structure of a dual quantum field theory appears in this context to generalize for de Sitter space–times as well.

Holographic codes from hyperinvariant tensor networks

Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code’s logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT, such as complementary recovery. However, the boundary states of such tensor networks typically do not exhibit the expected correlation functions of CFT boundary states. In this work, we show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states. Furthermore, these codes exhibit a state-dependent breakdown of complementary recovery as expected from AdS/CFT under small quantum gravity corrections.

Holographic Schwinger effect in an anisotropic background with Gauss-Bonnet corrections* *Supported in part by the National Key Research and Development Program of China (2022YFA1604900); partly supported by the National Natural Science Foundation of China (12275104, 11890711, 11890710, 11735007)

Using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, we study the holographic Schwinger effect in an anisotropic background with the Gauss-Bonnet term. As the background geometry is anisotropic, we consider both cases of the test particle pair and the electric field perpendicular to and parallel to the anisotropic direction. It is shown that the Schwinger effect is enhanced in the perpendicular case when anisotropy rises. In the parallel case, this effect is reversed. Additionally, the potential barrier and the critical electric field in the parallel case are more significantly modified by anisotropy compared to the perpendicular case. We also find that the presence of the Gauss-Bonnet coupling tends to increase the Schwinger effect.

Simple bulk reconstruction in anti-de Sitter/conformal field theory correspondence

Abstract In this paper, we show that bulk reconstruction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is rather simple and has an intuitive picture, by showing that the HKLL (Hamilton-Kabat-Lifschytz-Lowe) bulk reconstruction formula can be simplified. We also reconstruct the wave packets in the bulk theory from the CFT primary operators. With these wave packets, we discuss the causality and duality constraints and find our picture is the only consistent one. Our picture of the bulk reconstruction can be applied to the asymptotic AdS spacetime.

Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproducts

The Lie superalgebra psl(2|2) is recognized as a quite special algebra. In mathematics, it has the vanishing Killing form and allows for the three-dimensional central extension. In physics, it shows up as the symmetry of the one-dimensional Hubbard model and the asymptotic S-matrix of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra psl(2|2). Furthermore, we show that it possesses Hopf algebra structures, particularly the coproducts. The idea to prove the existence of manifest coproducts is as follows. First, we shall introduce them to Levendorskii’s realization, a system of a finite truncation of Drinfeld generators. Second, we show that Levendorskii’s realization is isomorphic to the Drinfeld realization by induction.

Tensor network models of AdS/qCFT

The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.

Comments on contact terms and conformal manifolds in the AdS/CFT correspondence

Abstract We study the contact terms that appear in the correlation functions of exactly marginal operators using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ a holographic renormalization group to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP–Witten prescription, and show that they match the expected results precisely. The cut-off surface prescription in the bulk serves as a regularization scheme for conformal perturbation theory in the boundary CFT. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.

Thermodynamics of soft wall model of AdS/QCD in Einstein–Maxwell–Gauss–Bonnet gravity

We investigate the thermodynamics of the confinement–deconfinement transition in the soft wall model of QCD with Gauss–Bonnet corrections using anti-de Sitter – conformal field theory (AdS/CFT) correspondence. In bulk AdS space–time the transition is geometric and is known as Hawking–Page transition. The Hawking–Page transition between two geometries, namely, charged AdS black hole and thermally charged AdS, have been studied with Gauss–Bonnet corrections up to first order. The Gauss–Bonnet coupling modifies the transition temperature of the system, but qualitative features remain unchanged. We obtain the curves between chemical potential and transition temperature for different values of Gauss–Bonnet couplings. We find that there exists a point in the μ–T plane where lines with different values of Gauss–Bonnet coupling cross. This point may be the onset of the transition from first-order to cross over behavior. The results are compared with that of the hard wall model.

Constraints on Symmetries from Holography.

In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti-de Sitter/conformal field theory correspondence. These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the nonperturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.

Measuring holographic entanglement entropy on a quantum simulator

Quantum simulation promises to have wide applications in many fields where problems are hard to model with classical computers. Various quantum devices of different platforms have been built to tackle the problems in, say, quantum chemistry, condensed matter physics, and high-energy physics. Here, we report an experiment towards the simulation of quantum gravity by simulating the holographic entanglement entropy. On a six-qubit nuclear magnetic resonance quantum simulator, we demonstrate a key result of Anti-de Sitter/conformal field theory (AdS/CFT) correspondence—the Ryu-Takayanagi formula is demonstrated by measuring the relevant entanglement entropies on the perfect tensor state. The fidelity of our experimentally prepared the six-qubit state is 85.0% via full state tomography and reaches 93.7% if the signal-decay due to decoherence is taken into account. Our experiment serves as the basic module of simulating more complex tensor network states that exploring AdS/CFT correspondence. As the initial experimental attempt to study AdS/CFT via quantum information processing, our work opens up new avenues exploring quantum gravity phenomena on quantum simulators.

Pontryagin Term and Magnetic Mass in 4D AdS Gravity

In the context of the anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, 4D AdS gravity is suitably renormalized by adding the Gauss Bonnet term to the Einstein-Hilbert action. The subsequent addition of the Pontryagin term, with a specific coupling, allows to write the on-shell action in terms of the Weyl tensor and its dual, such that the action becomes stationary for asymptotic (anti) self-dual solutions in the Weyl tensor. The addition to the action of both topological invariants mentioned above does not modify the bulk dynamics, but it does modify the expression of the Noether current and, therefore, the conserved quantities of the theory. Here, we show that the method of Iyer and Wald leads to a fully-covariant Noether charge, which contains both the electric and magnetic parts of the Weyl tensor. For configurations which are globally (anti) self-dual in the Weyl tensor, both the action and the Noether charge identically vanish. This means that, for such spacetimes, the magnetic mass is equal to the electric mass.

Discrete gravity on random tensor network and holographic R\xe9nyi entropy

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy Sn of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

Holographic superconductors in the presence of dark matter

The application of the gauge-gravity duality, also known as anti-de Sitter/conformal field theory (AdS/CFT) correspondence to study condensed matter systems has resulted in a number of important findings. Using the analogy, we have studied the phase transitions between a holographic insulator and a metal at zero temperature as well as finite temperature transition between a metal and a holographic superconductor of [Formula: see text]- and [Formula: see text]-wave symmetry. The main aim of this note is to look in which way the dark matter might affect the properties of superconductors. The hope is that some of the observed modifications could be used to detect this ubiquitous but still elusive component of matter in the Universe.

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

Highlighting the usefulness of string theory

Although Edward Witten does an admirable job explaining why the mathematical structure of string theory is quite beautiful (Physics Today, November 2015, page 38), I think he overstates the evidence that “string theory potentially unifies gravity with the other forces of nature.” In particular, it is unclear whether string theory provides a natural explanation for supersymmetry breaking or the observed properties of elementary particles. In addition, string theory has yet to explain how the unphysical predictions of classical general relativity are eliminated; for example, how the unphysical features of the interior Kerr metric—which describes the spacetime inside the event horizon of a rotating black hole—are eliminated in the course of the gravitational collapse of massive rotating objects.It is true that string theory has provided a nice model, the anti–de Sitter/ conformal field theory (AdS/CFT) correspondence, for the nature of spacetime just outside an event horizon, but to date string theory has had nothing definitive to say about the nature of spacetime inside an event horizon. A related problem for string theory (and also for classical general relativity) is that it provides no explanation for what the universe looked like prior to the Big Bang, which is unexpected if string theory really provides an underlying quantum theory of elementary particles and gravity.I completely agree with Witten that two-dimensional CFT is likely to have a critical role in any fundamental theory of spacetime. However, because of the obvious importance of four dimensions in the real world, it seems much more likely that four-dimensional curved twistor spaces11. R. S. Ward, R. O. Wells Jr, Twistor Geometry and Field Theory, Cambridge U. Press (1990). rather than strings play the role of fundamental objects.22. G. Chapline, K. Yamagishi, Phys. Rev. Lett. 66, 3064 (1991). https://doi.org/10.1103/PhysRevLett.66.3064 This, I submit, is an even more beautiful idea than string theory.REFERENCESSection:ChooseTop of pageREFERENCES <<1. R. S. Ward, R. O. Wells Jr, Twistor Geometry and Field Theory, Cambridge U. Press (1990). Google ScholarCrossref2. G. Chapline, K. Yamagishi, Phys. Rev. Lett. 66, 3064 (1991). https://doi.org/10.1103/PhysRevLett.66.3064, Google ScholarCrossref, ISI© 2016 American Institute of Physics.

Coherence length and magnetic penetration depth of the s-wave holographic superconductor model in Lifshitz spacetime

The AdS/CFT duality provides us a powerful guidance to study the strong-coupled conformal field theory by using its dual weak-coupled gravity. One of the interesting applications of the duality is to study high temperature superconductors, which are supposed to be a strongly coupled system. According to Ginzburg-Landau theory, a superconductor can be characterized by only two parameters, coherence length and the magnetic penetration length ; therefore, it is important to determine the two parameters. In this paper in the D=d+2-dimensional Lifshitz black hole, we analytically study the static fluctuation of the scalar field with nonzero spatial momentum along one spatial coordinate of the boundary, and investigate the perturbation of the gravitational system near the critical temperature Tc. Working in the probe limit (the gauge field and scalar field do not backreact on the original metric), we obtain the superconducting coherence length via AdS/CFT (anti-de Sitter/conformal field theory) correspondence, which is (1/Tc)(1-(T/Tc)-1/2. Moreover, in the probe limit (the magnetic field does not backreact to the background spacetime), we have calculated the diamagnetic current induced by a homogeneous external magnetic field perpendicular to the surface of the superconductor. Then, we obtain the magnetic penetration depth (Tc-T)-1/2, which agrees with the result in Ginzburg-Landau theory. And these results strongly support the idea that a superconductor can be described by a charged scalar field on the Lifshitz black hole via AdS/CFT (anti-de Sitter/conformal field theory) duality.

A holographic two-impurity Kondo model

We propose a model of a strongly-interacting two-impurity Kondo system based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. In a Landau Fermi Liquid, the single-impurity Kondo effect is the screening of an impurity spin at low temperature T . The two-impurity Kondo model then describes the competition between the Kondo interaction and the Heisenberg interaction between two impurity spins, also called the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. For spin-1/2 impurities, that competition leads to a quantum phase transition from a Kondo-screened phase to a phase in which the two impurity spins screen one another. Our holographic model is based on a (1 + 1)-dimensional CFT description of the two-impurity Kondo model, reliable for two impurities with negligible separation in space. We consider only impurity spins in a totally anti-symmetric representation of an SU(N ) spin symmetry. We employ a large-N limit, in which both Kondo and RKKY couplings are double-trace, and both Kondo and inter-impurity screening appear as condensation of single-trace operators at the impurities’ location. We perform the holographic renormalization of our model, which allows us to identify the Kondo and RKKY couplings as boundary conditions on fields in AdS. We numerically compute the phase diagram of our model in the plane of RKKY coupling versus T , finding evidence for a quantum phase transition from a trivial phase, with neither Kondo nor inter-impurity screening, to a non-trivial phase, with both Kondo and anti-ferromagnetic inter-impurity screening. More generally we show, just using SU(N ) representation theory, that ferromagnetic correlations must be absent at leading order in the large-N limit. Our holographic model may be useful for studying many open problems involving strongly-interacting quantum impurities, including for example the Kondo lattice, relevant for describing the heavy fermion compounds.

Study of the indirect interaction in a non-Fermi liquid within the AdS/CFT correspondence framework

The indirect spin–spin interaction between impurities in a non-Fermi quantum liquid system is theoretically investigated in this paper. The poles of the Green’s functions are shown to be responsible for the observed excitation spectra. Specifically, the anti-de Sitter/conformal field theory (AdS/CFT) correspondence is used to gain access to the analytical expressions of the Green’s functions for our particular problem.

A – c test of holography versus quantum renormalization group

We show that a "constructive derivation" of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence based on the quantum local renormalization group in large-N quantum field theories consistently provides the a – c holographic Weyl anomaly in d = 4 at the curvature squared order in the bulk action. The consistency of the construction further predicts the form of the metric beta function.