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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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We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two dimensional sigma-model. In the lowest order in $alpha$ we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.
There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal we use the vielbein and the connection without imposing the Weitzenb{o}ck connection. Then, we extract the teleparallel formulation of the theory by setting the curvature to null.
In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for the global translation and for the Nakanishis IOSp(8|8) choral symmetry containing the BRS symmetry as its member, are constructed. We generally show that for each of those Noether currents a suitable linear combination of equations of motion can be brought into the form of Maxwell-type field equation possessing the Noether current as its source term.
The Ryu-Takayanagi(RT) conjecture proposes that the entanglement entropy of a CFT in the large $c$ limit is equivalent to an area of an appropriate minimal surface in the dual bulk. However, there are some cases that RT conjecture predicts the entanglement entropy, which contradict to that of the corresponding CFT. In this paper, we present a refined gravity dual of the entanglement entropy of the large $c$ limit CFT as the sum of all the signed areas of cosmic branes satisfying a refined homologous condition.
The equations of motion for the position and spin of a classical particle coupled to an external electromagnetic and gravitational potential are derived from an action principle. The constraints insuring a correct number of independent spin components are automatically satisfied. In general the spin is not Fermi-Walker transported nor does the position follow a geodesic, although the deviations are small for most situations.
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