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Register a new userGravitation in flat spacetime from entanglement
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We explore holographic entanglement entropy for Minkowski spacetime in three and four dimensions. Under some general assumptions on the putative holographic dual, the entanglement entropy associated to a special class of subregions can be computed using an analog of the Ryu-Takayanagi formula. We refine the existing prescription in three dimensions and propose a generalization to four dimensions. Under reasonable assumptions on the holographic stress tensor, we show that the first law of entanglement is equivalent to the gravitational equations of motion in the bulk, linearized around Minkowski spacetime.
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In this note, we describe how collections of arbitrary numbers of BC-bits, distinct non-interacting quantum systems each consisting of a holographic boundary conformal field theory (BCFT), can be placed in multipartite entangled states in order to encode single connected bulk spacetimes that approximate geometries dual to holographic CFT states. The BC-bit version of a holographic CFT state corresponds to a geometry that can be made arbitrarily similar to the associated CFT-state geometry within a causal diamond region defined by points that are spacelike separated from the boundary time slice at which the state is defined. These holographic multi BC-bit states can be well-represented by tensor networks in which the individual tensors are associated with states of small numbers of BC-bits.
We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say $R$ and $L$ separated by another region, $C$. We are interested in the field theory in $Rcup L$ to understand the long range quantum correlations between $R$ and $L$. There are local modes of the Dirac field having supports individually either in $R$ or $L$, as well as global modes found via analytically continuing the $R$ modes to $L$ and vice versa. However, we show that unlike the case of a scalar field, the analytic continuation does not preserve the orthogonality of the resulting global modes. Accordingly, we need to orthonormalise them following the Gram-Schmidt prescription, prior to the field quantisation in order to preserve the canonical anti-commutation relations. We observe that this prescription naturally incorporates a spacetime independent continuous parameter, $theta_{rm RL}$, into the picture. Thus interestingly, we obtain a naturally emerging one-parameter family of $alpha$-like de Sitter vacua. The values of $theta_{rm RL}$ yielding the usual thermal spectra of massless created particles are pointed out. Next, using these vacua, we investigate both entanglement and Renyi entropies of either of the regions and demonstrate their dependence on $theta_{rm RL}$.
We consider a deformation of five-dimensional warped gravity with bulk and boundary mass terms to quadratic order in the action. We show that massless zero modes occur for special choices of the masses. The tensor zero mode is a smooth deformation of the Randall-Sundrum graviton wavefunction and can be localized anywhere in the bulk. There is also a vector zero mode with similar localization properties, which is decoupled from conserved sources at tree level. Interestingly, there are no scalar modes, and the model is ghost-free at the linearized level. When the tensor zero mode is localized near the IR brane, the dual interpretation is a composite graviton describing an emergent (induced) theory of gravity at the IR scale. In this case Newtons law of gravity changes to a new power law below the millimeter scale, with an exponent that can even be irrational.
Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators, which map a scalar field onto another massive scalar field. We construct such operators, in arbitrary dimensions, from closed conformal Killing vector fields, eigenvectors of the Ricci tensor. As an example, we explicitly construct these objects in anti-de Sitter spacetime (AdS) and show that they exist for masses above the Breitenlohner-Freedman (BF) bound. Starting from a regular seed solution of the massive Klein-Gordon equation (KGE), mass ladder operators in AdS allow one to build a variety of regular solutions with varying boundary condition at spatial infinity. We also discuss mass ladder operator in the context of spherical harmonics, and the relation between supersymmetric quantum mechanics and so-called Aretakis constants in an extremal black hole.
We study the effect of vortices on the tunneling decay of a symmetry-breaking false vacuum in three spacetime dimensions with gravity. The scenario considered is one in which the initial state, rather than being the homogeneous false vacuum, contains false vortices. The question addressed is whether, and, if so, under which circumstances, the presence of vortices has a significant catalyzing effect on vacuum decay. After studying the existence and properties of vortices, we study their decay rate through quantum tunneling using a variety of techniques. In particular, for so-called thin-wall vortices we devise a one-parameter family of configurations allowing a quantum-mechanical calculation of tunneling. Also for thin-wall vortices, we employ the Israel junction conditions between the interior and exterior spacetimes. Matching these two spacetimes reveals a decay channel which results in an unstable, expanding vortex. We find that the tunneling exponent for vortices, which is the dominant factor in the decay rate, is half that for Coleman-de Luccia bubbles. This implies that vortices are short-lived, making them cosmologically significant even for low vortex densities. In the limit of the vanishing gravitational constant we smoothly recover our earlier results for the decay of the false vortex in a model without gravity.
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