AdS-CFT Research Articles

An Uncertain Perspective on Consciousness

This should be considered as an addendum to Fundamental Cosmology and Physics Beyond the Standard Model [1] and ideas from pilot/wave theory [2]. It is more accurate to say that this is a philosophical perspective that comes from common basic observations and we can give a simple demonstration of this Pilot Wave theory by showing several examples of scale invariance [3]. It is not only just at the smallest levels of quantum mechanics we can observe these properties. Consider large flocks of birds or schools of fish moving together at the human scales of perception. We may show each bird is a particle being piloted by the wave of birds in the flock. But, each bird is also a small part of the wave and has the freedom to change the waveform simultaneously, dynamically. As some might say, “That’s all there is folks.” A living fish or bird, with simpleconsciousness, can change the waveform based on internal freewill. There is something happening internally that sets life apart from that which can only be influenced externally. Life has internal dynamics. Particles interacting at the sub-atomic level have no choice in their interaction with the waveform, as this is solely influenced by its own (external) properties. Indeed there is a Markov blanket separating internal and external states. There is a repeating pattern of scale invariance when comparing brain holography theory and ADS-CFT correspondence [4], as black hole holography, as we will show.

Multiscale Entanglement Renormalization Ansatz: Causality and Error Correction

Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator.

Quantum error-correction codes and absolutely maximally entangled states

The connection between maximally entangled states and quantum error-correcting code is explored to gain insight on the AdS-CFT correspondence, i.e., on the link between gravity and quantum field theories. The study presents corrections to the so-called Ryu-Takayanagi formula.

Sketching a proof of the Maldacena conjecture at small radius

At small AdS radius, the superstring on AdS5 × S5 was conjectured by Maldacena to be equivalent to mathcal{N} = 4 super-Yang-Mills at small ‘t Hooft coupling where thickened Feynman diagrams can be used to compute scattering amplitudes. It was previously shown that the pure spinor worldsheet action of the AdS5 × S5 superstring can be expressed as the sum of a BRST-trivial term and a “B-term” which is antisymmetric in worldsheet derivatives. Using the explicit form of the pure spinor vertex operators, it will be argued here that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the regions near the AdS horizon. Evidence will then be presented that the antisymmetric B-term generates the super-Yang-Mills vertex so that, at small radius and arbitrary genus, the superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram expansion.

AdS-CFT correspondence in noncommutative background, related thermodynamics and holographic superconductor in magnetic field

In this work, we formulate a non-commutative (NC) extension of AdS-CFT correspondence that is manifested in the modification of behavior of a holographic superconductor. The noncommutativity is introduced in the model through the NC corrected AdS charged black hole metric developed by Nicolini, Smailagic and Spallucci. First of all we discuss thermodynamic properties of this black hole in Euclidean formalism. In particular, we compute trace of the boundary energy-momentum tensor which, as expected, is non-zero due to the NC scale introduced in the model. Our findings indicate that the non-commutative effects tend to work against the black hole hair formation. This, in turn, has an adverse effect on the holographic superconductor by making the superconducting phase more fragile. This is reflected in the reduced value of the critical magnetic field and critical temperature. Finally, we comment on a qualitative agreement between our (holographic superconductor) result and that obtained for a conventional superconductor in NC space in a purely condensed matter scenario. In both cases noncommutativity tends to oppose the superconducting phase.

Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics

Huygens triviality – a concept invented by Jacques Hadamard – describes an equivalence class connecting those 2nd order partial differential equations which are transformable into the wave equation. In this work it is demonstrated, that the Schrödinger equation with the time-independent Hamiltonian belongs to such an equivalence class. The wave equation is the equation for which Huygens’ principle (HP) holds. The HP was a subject of confusion in both physics and mathematics literature for a long time. Not surprisingly, the role of this principle was obscured from the beginnings of quantum mechanics causing some theoretical and experimental misunderstandings. The purpose of this work is to bring the full clarity into this topic. By doing so, we obtained a large amount of new results related to uses of Lie sphere geometry, of twistors, of Dupin cyclides, of null electromagnetic fields, of AdS-CFT correspondence, of Penrose limits, of geometric algebra, etc. in physical problems ranging from the atomic to high energy physics and cosmology.

Duality in an asset exchange model for wealth distribution

Asset exchange models are agent-based economic models with binary transactions. Previous investigations have augmented these models with mechanisms for wealth redistribution, quantified by a parameter χ, and for trading bias favoring wealthier agents, quantified by a parameter ζ. By deriving and analyzing a Fokker–Planck equation for a particular asset exchange model thus augmented, it has been shown that it exhibits a second-order phase transition at ζ∕χ=1, between regimes with and without partial wealth condensation. In the “subcritical” regime with ζ∕χ<1, all of the wealth is classically distributed; in the “supercritical” regime with ζ∕χ>1, a fraction 1−χ∕ζ of the wealth is condensed. Intuitively, one may associate the supercritical, wealth-condensed regime as reflecting the presence of “oligarchy,” by which we mean that an infinitesimal fraction of the total agents hold a finite fraction of the total wealth in the continuum limit.In this paper, we further elucidate the phase behavior of this model – and hence of the generalized solutions of the Fokker–Planck equation that describes it – by demonstrating the existence of a remarkable symmetry between its supercritical and subcritical regimes in the steady-state. Noting that the replacement {ζ→χ,χ→ζ}, which clearly has the effect of inverting the order parameter ζ∕χ, provides a one-to-one correspondence between the subcritical and supercritical states, we demonstrate that the wealth distribution of the subcritical state is identical to that of the corresponding supercritical state when the oligarchy is removed from the latter. We demonstrate this result analytically, both from the microscopic agent-level model and from its macroscopic Fokker–Planck description, as well as numerically. We argue that this symmetry is a kind of duality, analogous to the famous Kramers–Wannier duality between the subcritical and supercritical states of the Ising model, and to the Maldacena duality that underlies AdS/CFT theory.

Geodesically complete metrics and boundary non-locality in holography: Consequences for the entanglement entropy

We show explicitly that the full structure of IIB string theory is needed to remove the non-localities that arise in boundary conformal theories that border hyperbolic spaces on AdS$_5$. Specifically, using the Caffarelli/Silvestri\cite{caffarelli}, Graham/Zworski\cite{graham}, and Chang/Gonzalez\cite{chang:2010} extension theorems, we prove that the boundary operator conjugate to bulk p-forms with negative mass in geodesically complete metrics is inherently a non-local operator, specifically the fractional conformal Laplacian. The non-locality, which arises even in compact spaces, applies to any degree p-form such as a gauge field. We show that the boundary theory contains fractional derivatives of the longitudinal components of the gauge field if the gauge field in the bulk along the holographic direction acquires a mass via the Higgs mechanism. The non-locality is shown to vanish once the metric becomes incomplete, for example, either 1) asymptotically by adding N transversely stacked Dd-branes or 2) exactly by giving the boundary a brane structure and including a single transverse Dd-brane in the bulk. The original Maldacena conjecture within IIB string theory corresponds to the former. In either of these proposals, the location of the Dd-branes places an upper bound on the entanglement entropy because the minimal bulk surface in the AdS reduction is ill-defined at a brane interface. Since the brane singularities can be circumvented in the full 10-dimensional spacetime, we conjecture that the true entanglement entropy must be computed from the minimal surface in 10-dimensions, which is of course not minimal in the AdS$_5$ reduction.

Black hole phase transitions and the chemical potential

In the context of extended phase space thermodynamics and the AdS-CFT correspondence, we consider the chemical potential ($\mu$) dual to the number of colours ($N$) of the boundary gauge theory, in the grand canonical ensemble. By appropriately defining $\mu$ via densities of thermodynamic quantities, we show that it changes sign precisely at the Hawking-Page transition for AdS-Schwarzschild and RN-AdS black holes in five dimensions, signalling the onset of quantum effects at the transition point. Such behaviour is absent for non-rotating black holes in four dimensions. For Kerr-AdS black holes in four and five dimensions, our analysis points to the fact that $\mu$ can change sign in the stable black hole region, i.e above the Hawking-Page transition temperature, for a range of angular frequencies. We also analyse AdS black holes in five dimensional Gauss-Bonnet gravity, and find similar features for $\mu$ as in the Kerr-AdS case.

Free-energy analysis of spin models on hyperbolic lattice geometries.

We investigate relations between spatial properties of the free energy and the radius of Gaussian curvature of the underlying curved lattice geometries. For this purpose we derive recurrence relations for the analysis of the free energy normalized per lattice site of various multistate spin models in the thermal equilibrium on distinct non-Euclidean surface lattices of the infinite sizes. Whereas the free energy is calculated numerically by means of the corner transfer matrix renormalization group algorithm, the radius of curvature has an analytic expression. Two tasks are considered in this work. First, we search for such a lattice geometry, which minimizes the free energy per site. We conjecture that the only Euclidean flat geometry results in the minimal free energy per site regardless of the spin model. Second, the relations among the free energy, the radius of curvature, and the phase transition temperatures are analyzed. We found out that both the free energy and the phase transition temperature inherit the structure of the lattice geometry and asymptotically approach the profile of the Gaussian radius of curvature. This achievement opens new perspectives in the AdS-CFT correspondence theories.

The Holographic Universe

How is a black hole in a 5-D anti de Sitter space like a flat 4-D field of particles and radiation? Jean-Pierre Luminet explains the holographic principle, the Maldacena conjecture, and the resolution of the information paradox.

Supersymmetry on a Lattice

Attempts to formulate supersymmetric field theories on discrete spacetime lattices have a long history. However, until recently most of these efforts have failed. In this talk I will review some of the new ideas that have finally allowed a solution to this problem for certain supersymmetric theories. I will focus my attention, in particular, on N=4 super Yang-Mills which forms one of the pillars of the AdSCFT correspondence connecting gravitational theories in anti-deSitter space to gauge theories living on the boundary of that space. It is also integral to the scattering amplitudes program and is under intensive study using conformal bootstrap techniques. I will review the theoretical construction of the model and describe what is known analytically about the lattice theory. Following on from this I will present preliminary results stemming from the first large scale lattice study of N=4 Yang-Mills. Our results are consistent with the existence of a single deconfined phase for the theory in which the static fermion potential shows only a Coulomb-like behavior. Unlike QCD there is no confining, chirally broken phase even at strong coupling.

The Einstein–Klein–Gordon–AdS system for general boundary conditions

We construct unique local solutions for the spherically-symmetric Einstein–Klein–Gordon–anti-de Sitter (AdS) system subject to a large class of initial and boundary conditions including some considered in the context of the AdS-CFT correspondence. The proof relies on estimates developed for the linear wave equation by the second author and involves a careful renormalization of the dynamical variables, including a renormalization of the well-known Hawking mass. For some of the boundary conditions considered this system is expected to exhibit rich global dynamics, including the existence of hairy black holes. This paper furnishes a starting point for such global investigations.

Ads-CFT correspondence in dilaton coupled n dimensional black holes

We establish AdS-CFT correspondence for n-dimensional AdS dilaton coupled black hole. Following two different approaches to establish the correspondence we calculate the energy from supergravity theory as well as boundary two point function from bulk geodesic.

Gauge symmetries and holographic anomalies of Chern-Simons and transgression AdS gravity

We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.

The Ongoing Impact of Modular Localization on Particle Theory

Modular localization is the concise conceptual formulation of causal localization in the setting of local quantum physics. Unlike QM it does not refer to individual operators but rather to ensembles of observables which share the same localization region, as a result it explains the probabilistic aspects of QFT in terms of the impure KMS nature arising from the local restriction of the pure vacuum. Whereas it played no important role in the perturbation theory of low spin particles, it becomes indispensible for interactions which involve higher spin $s\geq1$ fields, where is leads to the replacement of the operator (BRST) gauge theory setting in Krein space by a new formulation in terms of stringlocal fields in Hilbert space. The main purpose of this paper is to present new results which lead to a rethinking of important issues of the Standard Model concerning massive gauge theories and the Higgs mechanism. We place these new findings into the broader context of ongoing conceptual changes within QFT which already led to new nonperturbative constructions of models of integrable QFTs. It is also pointed out that modular localization does not support ideas coming from string theory, as extra dimensions and Kaluza-Klein dimensional reductions outside quasiclassical approximations. Apart from hologarphic projections on null-surfaces, holograhic relations between QFT in different spacetime dimensions violate the causal completeness property, this includes in particular the Maldacena conjecture. Last not least, modular localization sheds light onto unsolved problems from QFT's distant past since it reveals that the Einstein-Jordan conundrum is really an early harbinger of the Unruh effect.

Gauge-Gravity Duality and the Black Hole Interior

We present a further argument that typical black holes with field theory duals have firewalls at the horizon. This argument makes no reference to entanglement between the black hole and any distant system, and so is not evaded by identifying degrees of freedom inside the black hole with those outside. We also address the Einstein-Rosen=Einstein-Podolsky-Rosen conjecture of Maldacena and Susskind, arguing that the correlations in generic highly entangled states cannot be geometrized as a smooth wormhole.

On the matching method and the Goldstone theorem in holography

We study the transition of a scalar field in a fixed $AdS_{d+1}$ background between an extremum and a minimum of a potential. We compute analytically the solution to the perturbation equation for the vev deformation case by generalizing the usual matching method to higher orders and find the propagator of the boundary theory operator defined through the AdS-CFT correspondence. We show that, contrary to what happens at the leading order of the matching method, the next-to-leading order presents a simple pole at $q^2=0$ in accordance with the Goldstone theorem applied to a spontaneously broken dilatation invariance.

Multipoint correlators of conformal field theories: Implications for quantum critical transport

We compute three-point correlators between the stress-energy tensor and the conserved currents of conformal field theories (CFTs) in 2+1 dimensions. We first compute the correlators in the large-flavor-number expansion of conformal gauge theories and then perform the computation using holography. In the holographic approach, the correlators are computed from an effective action on (3+1)-dimensional anti-de Sitter space (${\mathrm{AdS}}_{4}$) and depend upon the coefficient $\ensuremath{\gamma}$ of a four-derivative term in the action. We find a precise match between the CFT and the holographic results, thus, fixing the values of $\ensuremath{\gamma}$. The CFTs of free fermions and bosons take the values $\ensuremath{\gamma}=1/12,\ensuremath{-}1/12$, respectively, and so saturate the bound $|\ensuremath{\gamma}|\ensuremath{\le}1/12$ obtained earlier from the holographic theory; the correlator of the conserved gauge flux of $U(1)$ gauge theories takes intermediate values of $\ensuremath{\gamma}$. The value of $\ensuremath{\gamma}$ also controls the frequency dependence of the conductivity and other properties of quantum critical transport at nonzero temperatures. Our results for the values of $\ensuremath{\gamma}$ lead to an appealing physical interpretation of particlelike or vortexlike transport near quantum phase transitions of interest in condensed-matter physics. This paper includes Appendices reviewing key features of the AdS-CFT correspondence for condensed-matter physicists.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.