arXiv subjects

Benjamin Mosk

Publications and source records attributed to Benjamin Mosk.

9 recordsLinked to original sources

arXiv2017

Metric Perturbations of Extremal Surfaces

Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, thereby providing a closed form expression for the canonical energy. We find that a perturbation governed by some small parameter $\lambda$ yields an expansion of the surface area in terms of a highly non-local expression involving multiple integrals of geometric quantities over the original extremal surface.

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arXiv2016

Equivalent Equations of Motion for Gravity and Entropy

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter pace. In doing so, we make use of the formalism of kinematic space [arXiv:1505.05515] and fields on this space, introduced in [arXiv:1604.03110]. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

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arXiv2016

Holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations

We use the intertwining properties of integral transformations to provide a compact proof of the holographic equivalence between the first law of entanglement entropy and the linearized gravitational equations, in the context of the AdS/CFT-correspondence. We build upon the framework developed by Faulkner et al. [1] using the the Wald formalism, and exploit the symmetries of the vacuum modular Hamiltonian of ball-shaped boundary regions.

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arXiv2016

A Stereoscopic Look into the Bulk

We present the foundation for a holographic dictionary with depth perception. The dictionary consists of natural CFT operators whose duals are simple, diffeomorphism-invariant bulk operators. The CFT operators of interest are the "OPE blocks," contributions to the OPE from a single conformal family. In holographic theories, we show that the OPE blocks are dual at leading order in 1/N to integrals of effective bulk fields along geodesics or homogeneous minimal surfaces in anti-de Sitter space. One widely studied example of an OPE block is the modular Hamiltonian, which is dual to the fluctuation in the area of a minimal surface. Thus, our operators pave the way for generalizing the Ryu-Takayanagi relation to other bulk fields. Although the OPE blocks are non-local operators in the CFT, they admit a simple geometric description as fields in kinematic space--the space of pairs of CFT points. We develop the tools for constructing local bulk operators in terms of these non-local objects. The OPE blocks also allow for conceptually clean and technically simple derivations of many results known in the literature, including linearized Einstein's equations and the relation between conformal blocks and geodesic Witten diagrams.

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arXiv2016

Orthogonal Nilpotent Superfields from Linear Models

We derive supersymmetry/supergravity models with constrained orthogonal nilpotent superfields from the linear models in the formal limit where the masses of the sgoldstino, inflatino and sinflaton tend to infinity. The case where the sinflaton mass remains finite leads to a model with a `relaxed' constraint, where the sinflaton remains an independent field. Our procedure is equivalent to a requirement that some of the components of the curvature of the moduli space tend to infinity.

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arXiv2015

Vacua and correlators in hyperbolic de Sitter space

We study the power - and bi -spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one -parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch -Davies vacuum state. Selecting the Bunch -Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch -Davies state the hyperbolic de Sitter $n$-point correlation functions have to match the planar de Sitter $n$-point correlation functions. The expressions for the planar and hyperbolic Bunch -Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power - and bi -spectrum. For the bi -spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch -Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.

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arXiv2014

Casting Shadows on Holographic Reconstruction

In the context of the AdS/CFT correspondence, we study several holographic probes that relate information about the bulk spacetime to CFT data. The best-known example is the relation between minimal surfaces in the bulk and entanglement entropy of a subregion in the CFT. Building on earlier work, we identify "shadows" in the bulk: regions that are not illuminated by any of the bulk probes we consider, in the sense that the bulk surfaces do not pass through these regions. We quantify the size of the shadow in the near horizon region of a black hole and in the vicinity of a sufficiently dense star. The existence of shadows motivates further study of the bulk-boundary dictionary in order to identify CFT quantities that encode information about the shadow regions in the bulk. We speculate on the interpretation of our results from a dual field theory perspective.

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arXiv2014

Chaotic inflation limits for non-minimal models with a Starobinsky attractor

We investigate inflationary attractor points by analyzing non-minimally coupled single field inflation models in two opposite limits; the `flat' limit in which the first derivative of the conformal factor is small and the `steep' limit, in which the first derivative of the conformal factor is large. We consider a subset of models that yield Starobinsky inflation in the steep conformal factor, strong coupling, limit and demonstrate that they result in chaotic inflation in the opposite flat, weak coupling, limit. The suppression of higher order powers of the inflaton field in the potential is shown to be related to the flatness condition on the conformal factor. We stress that the chaotic attractor behaviour in the weak coupling limit is of a different, less universal, character than the Starobinsky attractor. Agreement with the COBE normalisation cannot be obtained in both attractor limits at the same time and in the chaotic attractor limit the scale of inflation depends on the details of the conformal factor, contrary to the strong coupling Starobinsky attractor.

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arXiv2013

Properties of Causal Holographic Information

Causal holographic information [1] is a variant of the Ryu-Takayanagi proposal for the entanglement entropy of a spatial region in the context of AdS/CFT, but with the bulk surface defined by causality rather than extremality. We investigate the properties of causal holographic information, focusing in particular on the universal coefficient of the logarithmically divergent term. We find that this coefficient contains a novel conformal invariant that cannot be written as an integral of local quantities. By considering higher curvature corrections in the bulk, we identify the coefficient of the a and c central charges in 4 dimensions. Finally, we speculate about which CFT quantity could correspond to the causal holographic information.

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