Holographic dual approach to magnetism and magnetization dynamics

We introduce a new approach to understand magnetization dynamics in\nferromagnets based on the holographic realization of ferromagnets. A\nLandau-Lifshitz equation describing the magnetization dynamics is derived from\na Yang-Mills equation in the dual gravitational theory, and temperature\ndependences of the spin-wave stiffness and spin transfer torque appearing in\nthe holographic Landau-Lifshitz equation are investigated by the holographic\napproach. The results are consistent with the known properties of magnetization\ndynamics in ferromagnets with conduction electrons.\n

Spin-pumping across ferromagnet/superconductor (F/S) interfaces has attracted much attention lately. Yet the focus has been mainly on s-wave superconductors-based systems whereas (high-temperature) d-wave superconductors such as YBa2Cu3O7-d (YBCO) have received scarce attention despite their fundamental and technological interest. Here we use wideband ferromagnetic resonance to study spin-pumping effects in bilayers that combine a soft metallic Ni80Fe20 (Py) ferromagnet and YBCO. We evaluate the spin conductance in YBCO by analyzing the magnetization dynamics in Py. We find that the Gilbert damping exhibits a drastic drop as the heterostructures are cooled across the normal-superconducting transition and then, depending on the S/F interface morphology, either stays constant or shows a strong upturn. This unique behavior is explained considering quasiparticle density of states at the YBCO surface, and is a direct consequence of zero-gap nodes for particular directions in the momentum space. Besides showing the fingerprint of d-wave superconductivity in spin-pumping, our results demonstrate the potential of high-temperature superconductors for fine tuning of the magnetization dynamics in ferromagnets using k-space degrees of freedom of d-wave/F interfaces.

We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.

The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) - a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size - the scale of non-locality in the PFT - and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen - a throat in the geometry - that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces - akin to other non-local settings that employ quantum group structures.

A five-dimensional Chern–Simons gravity theory based on the anti-de Sitter group SO (4, 2) is argued to be a useful model in which to understand the details of holography and the relationship between generally covariant and dual local quantum field theories. Defined on a manifold with boundary, conformal geometry arises naturally as a gauge invariance preserving boundary condition. By matching thermodynamic quantities for a particular background geometry, the dimensionless coupling constant of the Chern–Simons theory is directly related to the number of fields in a putative dual theory at high temperature. As a consistency check, the semiclassical factorization of Wilson line observables in the gravity theory is shown to induce a factorization in dual theory observables as expected by general arguments of large-N gauge theory.

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy’s formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy’s formula. We follow an effective field theory approach and consider the Kerr–Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.

Holographic dark energy

In this work we study the Dirac quasinormal modes of higher dimensional charged black holes. Higher dimensional Reissner–Nordström type black holes as well as charged black holes in Einstein–Gauss–Bonnet theories are studied for fermionic perturbations using WKB method. A comparative study of the quasinormal modes in the two different theories of gravity has been performed. The behavior of the frequencies with the variation of black hole parameters as well as with the variation of space-time dimensions is studied. We also study the large multipole number limit of the black hole potential in order to look for an analytic expression for the frequencies.

In this paper we systematically develop the flat/CFT holographic dictionary, building on AdS/CFT holography. After analysing the behaviour of scalar field modes on hyperbolic slices of Minkowski and performing the holographic renormalisation for the associated onshell action, we obtain a holography dictionary between the bulk theory and the corresponding dual theory on the celestial sphere. We propose that a single scalar field in the bulk is dual to two series of operators on the celestial sphere; the scaling dimension of these operators takes values on the principal series. The real time features of the bulk theory, such as the dynamical and the casual structure, are encoded in the construction of correlation functions on the boundary via the coefficients of the bulk modes. Moreover, we will see that the two series of operators can be interpreted as ingoing and outgoing waves in the bulk. We illustrate our dictionary with the example of a single shock wave. Our results lay foundations for further computation within the flat/celestial CFT correspondence.

In this thesis, the author studies the information loss problem using semi-classical black holes. If a black hole loses information after evaporation, it will imply the violation of unitarity and predictability. Therefore, to understand the nature of the Theory of Everything and to reconcile the quantum theory and gravitation, we need to understand the problem of the information loss. If we assume that there exists a unitary theory of quantum gravity as a working hypothesis, the area of a black hole is proportional to the statistical entropy of the black hole, and there is an observer who can see information from Hawking radiation, then it is inevitable to accept black hole complementarity. However, if there is an observer who can see both information of inside and outside, i.e., if the duplication experiment is possible, then black hole complementarity will be violated. A duplication experiment and other thought experiments can be investigated by semi-classical backgrounds. In this thesis, we focus on three subjects: gravitational objects of Einstein gravity with renormalized energy-momentum tensors, gravitational objects of modified theories of gravity, and initial conditions which can be prepared by quantum tunneling. To study such subjects, we use the following techniques: traditional analytic approaches, numerical approaches using the double-null formalism, and Euclidean analytic continuations. We study a possibility of a duplication experiment in a charged black hole and a regular black hole. Causal structures allow the possibility; but to regularize curvatures around the inner horizon, we require a sufficiently large number of massless fields which contribute to Hawking radiation. In fact, if we assume the large number, we can violate black hole complementarity even for neutral black holes. The required number of fields can be reduced to a reasonable amount; although we need a large number, if it is finite, the number may be allowed by a model of quantum gravity including string theory. This suggests that the area of the black hole may not imply the statistical entropy of the internal and physical degrees of freedom and there may be no observer who can read information via Hawking radiation. Also, we study a possibility of a formation of a bubble universe. The author used weaker assumptions than previous authors to obtain bubble universes. The Brans-Dicke theory can allow a false vacuum bubble as an instanton solution and such a theory may be allowed by quantum gravity including string theory. False vacuum bubbles will emit negative energy along the out-going direction and such negative energy can be used to obtain a bubble universe. Although we have to check whether these scenarios are possible in realistic quantum gravity, if it is possible, then it will strongly support a loss of information and a violation of unitarity at least in the ‘effective’ sense. These conclusions imply that, if there exists a unitary theory of quantum gravity or the Theory of Everything, we will observe a lose of information and a violation of unitarity in the ‘effective’ way.

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many body system with random all-to-all interactions on fermionic N sites (N>>1). This model is shown to saturate the known maximal chaos bound of many body system and then based on this observation it is conjectured to be dual to a quantum black hole in the sense of the AdS/CFT correspondence. In this dissertation, we show that the large N physics of the SYK model is systematically described by a single bi-local field. In particular, we emphasize the appearance of the emergent conformal reparametrization symmetry at the critical IR fixed point and the corresponding divergent contribution of the symmetry modes in the propagator of the bi-local field. We discuss non-linear-level derivation of the zero modes effective action, which is given by the Schwarzian derivative for finite reparametrization symmetry. Besides the symmetry modes, which correspond to the dilaton-gravity sector in the dual AdS theory, the SYK model also predicts an infinite tower of matter fields in AdS_2. We demonstrate that this infinite spectrum can be nicely packaged into a single field in 3-dimensional space-time. Finally, we consider the question of identifying the dual space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green's functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2D string theory.

The charged black hole thermodynamics is corrected in terms of the quantum gravity effects. Most of the quantum gravity theories support the idea that near the Planck scale, the standard Heisenberg uncertainty principle should be reformulated by the so-called Generalized Uncertainty Principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of the minimal length and maximal momentum as GUP type I and the minimal length, minimal momentum and maximal momentum as GUP type II on thermo dynamics of the charged TeV-scale black holes. We also generalized our study to the universe with the extra dimensions based on the ADD model. In this framework, the effect of the electrical charge on thermodynamics of the black hole and existence of the charged black hole remnants as a potential candidate for the dark matter particles are discussed.

The gauge theory for the Poincare -Weyl group is constructed. It is shown that tetrads are not true gauge fields, but are functions of the true gauge fields: rotational, translational and dilatational ones. The equations of gauge fields, whose sources are an energy-momentum tensor, orbital and spin momemta as well as a dilatational current of an external field, are obtained. A new direct interaction of the rotational gauge field with the orbital momentum of an external field appears, which describes some new effects connected with the space gyroscope Probe B experiment.

Within the context of Newton’s theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a n-hypervolume where gravitation takes origin, within a n-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and “glue” to the central body via unification of the four known interactions and, in addition, 1) particles can no longer be conceived as point-like but e.g., strings or membranes, and 2) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.