We consider a set of observers who live near the boundary of global AdS, and are allowed to act only with simple low-energy unitaries and make measurements in a small interval of time. The observers are not allowed to leave the near-boundary region. We describe a physical protocol that nevertheless allows these observers to obtain detailed information about the bulk state. This protocol utilizes the leading gravitational back-reaction of a bulk excitation on the metric, and also relies on the entanglement-structure of the vacuum. For low-energy states, we show how the near-boundary observers can use this protocol to completely identify the bulk state. We explain why the protocol fails completely in theories without gravity, including non-gravitational gauge theories. This provides perturbative evidence for the claim that one of the signatures of holography - the fact that information about the bulk is also available near the boundary - is already visible in the low-energy theory of gravity.

In this paper, we present a simple and iterative algorithm that computes Witten diagrams. We focus on the gauge correlators in AdS in four dimensions in momentum space. These new combinatorial relations will allow one to generate tree level amplitudes algebraically, without having to do any explicit bulk integrations; hence, leading to a simple method of calculating higher point gauge amplitudes.

We study the spectral representation of finite temperature, out of time ordered (OTO) correlators on the multi-time-fold generalised Schwinger-Keldysh contour. We write the contour-ordered correlators as a sum over time-order permutations acting on a fundamental array of Wightman correlators. We decompose this Wightman array in a basis of column vectors, which provide a natural generalisation of the familiar retarded-advanced basis in the finite temperature Schwinger-Keldysh formalism. The coefficients of this decomposition take the form of generalised spectral functions, which are Fourier transforms of nested and double commutators. Our construction extends a variety of classical results on spectral functions in the SK formalism at finite temperature to the OTO case.Here ω p = p 2 + m 2 . The spectral function is also directly related to the Fourier-transform of commutators in the theory, viz., p ρ p e ip·(x 1 −x 2 ) = [φ(x 1 ), φ(x 2 )]

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice. These wavefunctionals must obey a set of constraints as a consequence of the diffeomorphism invariance of the theory, the most important of which is known as the Wheeler-DeWitt equation. We study these constraints perturbatively by expanding them to leading nontrivial order in Newton’s constant about a background AdS spacetime. We show that, even within perturbation theory, any wavefunctional that solves these constraints must have specific correlations between a component of the metric at infinity and energetic excitations of matter fields or transverse-traceless gravitons. These correlations disallow strictly localized excitations. We prove perturbatively that two states or two density matrices that coincide at the boundary for an infinitesimal interval of time must coincide everywhere in the bulk. This analysis establishes a perturbative version of holography for theories of gravity coupled to matter in AdS.

In this paper, we explore momentum space approach to computing scalar amplitudes in anti-de Sitter (AdS) space. We show that the algorithm derived by Arkani-Hamed, Benincasa, and Postnikov for cosmological wave functions can be straightforwardly adopted for AdS transition amplitudes in momentum space, allowing one to bypass bulk point integrations. We demonstrate the utility of this approach in AdS by presenting several explicit results both at tree and loop level.

Enstatite Mg 2 Si 2 O 6 is an important rock-forming silicate of the pyroxene group. It exists in several polymorphs, the structures of which are characterized by double ͓MgO 6 ͔ octahedral bands and single silicate chains. This paper reports lattice-dynamical rigid-ion model calculations and polarized Raman and inelasticneutron-scattering measurements of orthoenstatite Mg 2 Si 2 O 6 , which is orthorhombic ( Pbca) with 80 atoms in the unit cell. The calculated elastic constants, phonon frequencies, density of states, and specific heat are in good agreement with the experimental data. The optical-phonon branches along the ⌺ and ⌬ directions are relatively flat without significant dispersion, but have moderate dispersion along the ⌳ direction, reflecting the strong structural anisotropy in orthoenstatite. Orthoenstatite undergoes a displacive-reconstructive phase transformation at ϳ1360 K to protoenstatite Mg 2 Si 2 O 6 , which is also orthorhombic ( Pbcn) with 40 atoms in the unit cell and the a dimension half that of orthoenstatite. However, the computed phonon-dispersion relations in orthoenstatite do not exhibit any lattice instability in the entire Brillouin zone. The calculations predict that at the ⌫ point the lowest optic A g mode involving translations of Mg 2ϩ ions and translations and rotations of the tetrahedral silicate groups softens from 104 cm Ϫ1 in protoenstatite to 82 cm Ϫ1 in orthoenstatite, which is consistent with the single-crystal polarized Raman-scattering measurements. The phonon spectra obtained from inelastic-neutron-scattering measurements have been interpreted on the basis of model calculations. The broad peak in the 20-80-meV range in orthoenstatite is mainly due to Mg translations and the librations of the nearly rigid tetrahedral ͓SiO 4 ͔ groups, whereas the internal Si-O bond stretching vibrations of the ͓SiO 4 ͔ groups contribute mainly above 80 meV. The bridging oxygens in the silicate chains are vibrationally distinct from the nonbridging oxygens, leading to significant differences in the vibrational spectra of orthoenstatite and protoenstatite with tetrahedral silicate chains from those in forsterite Mg 2 SiO 4 with isolated silicate tetrahedra. The band gaps found in the phonon density of states of forsterite are filled by the vibrations of the bridging oxygens in the silicate chains in the phonon densities of states of orthoenstatite and protoenstatite.

An uniformly accelerated (Rindler) observer will detect particles in the Minkowski vacuum, known as Unruh effect. The spectrum is thermal and the temperature is given by that of the Killing horizon, which is proportional to the acceleration. Considering these particles are kept in a thermal bath with this temperature, we find that the correlation function of the random force due to radiation acting on the particles as measured by the accelerated frame, shows the fluctuation-dissipation relation. It is observed that the correlations, in both (1 + 1) spacetime and (1 + 3) dimensional spacetimes, are of Brownian type. We discuss the implications of this new observation at the end.

No abstract