Giorgos Anastasiou

We describe a method to generate scalar–tensor theories with Weyl symmetry, starting from arbitrary purely metric higher derivative gravity theories. The method consists in the definition of a conformally-invariant metric, that is a rank (0, 2)-tensor constructed out of the metric tensor and the scalar field. This new object has zero conformal weight and is given by, where is the conformal dimension of the scalar. As has conformal dimension of 2, the resulting tensor is trivially a conformal invariant. Then, the generated scalar–tensor theory, which we call the Weyl uplift of the original purely metric theory, is obtained by replacing the metric by in the action that defines the original theory. This prescription allowed us to define the Weyl uplift of theories with terms of higher order in the Riemannian curvature. Furthermore, the prescription for scalar–tensor theories coming from terms that have explicit …

We present a streamlined proof that any Einstein-AdS space is a solution of the Lu, Pang and Pope conformal gravity theory in six dimensions. The reduction of conformal gravity into Einstein theory manifestly shows that the action of the latter can be written as the Einstein-Hilbert term plus the Euler topological density and an additional contribution that depends on the Laplacian of the bulk Weyl tensor squared. The prescription for obtaining this form of the action by embedding the Einstein theory into a Weyl-invariant purely metric theory, was dubbed Conformal Renormalization and its resulting action was shown to be equivalent to the one obtained by holographic renormalization. As a non-trivial application of the method, we compute the Noether-Wald charges and thermodynamic quantities for topological black hole solutions with generic transverse section in Einstein-AdS 6 theory.

We study a conformally coupled scalar-tensor theory with a quartic potential possessing local conformal symmetry up to a boundary term. We show that requiring the restoration of the full local conformal symmetry fixes the counterterms that render the on-shell action finite. The building block of the resulting action is a conformally covariant tensor which is constructed out of the metric and the scalar field and it has the same conformal weight as the Weyl tensor. This allows us to obtain the counterterms for the scalar-tensor sector in a closed form. The finiteness of the conformally complete version of the action is suggestive on the validity of the conformal renormalization prescription. We extend this theory by adding the conformal gravity action and also the Einstein-AdS action written in MacDowell-Mansouri form. Even though the latter breaks the conformal symmetry, we find that the action is still renormalized provided a …

We find a covariant expression for the universal part of the holographic entanglement entropy which is valid for CFTs dual to generic higher curvature gravities in up to five bulk dimensions. We use this functional to compute universal coefficients of stress-tensor correlators in three-dimensional CFTs dual to Cubic Curvature Gravity. Using gauge/gravity duality, we work out an expression for the entanglement entropy of deformed entangling regions and read the coefficients from the power expansion of the entropy in the deformation parameter. In particular, we obtain the t 4 coefficient of the 3-point function and exhibit a difference between the results obtained using the entanglement entropy functional for minimal and non-minimal splittings. We compare the obtained expressions for t 4 derived considering both splittings with results obtained through other holographic methods which are splitting-independent. We find …

We provide a new derivation of the Hawking mass and Willmore energy functionals for asymptotically AdS spacetimes, by embedding Einstein-AdS gravity in Conformal Gravity. By construction, the evaluation of the four-dimensional Conformal Gravity action in a manifold with a conical defect produces a codimension-2 conformal invariant functional L Σ. The energy functionals are then particular cases of L Σ for Einstein-AdS and pure AdS ambient spaces, respectively. The bulk action is finite for AdS asymptotics and both Hawking mass and Willmore energy are finite as well. The result suggests a generic relation between conformal invariance and renormalization, where the codimension-2 properties are inherited from the bulk gravity action.

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory—originally found by Lu, Pang and Pope (LPP)—can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS …

We study the renormalization of Entanglement Entropy in holographic CFTs dual to Lovelock gravity. It is known that the holographic EE in Lovelock gravity is given by the Jacobson-Myers (JM) functional. As usual, due to the divergent Weyl factor in the Fefferman-Graham expansion of the boundary metric for Asymptotically AdS spaces, this entropy functional is infinite. By considering the Kounterterm renormalization procedure, which utilizes extrinsic boundary counterterms in order to renormalize the on-shell Lovelock gravity action for AAdS spacetimes, we propose a new renormalization prescription for the Jacobson-Myers functional. We then explicitly show the cancellation of divergences in the EE up to next-to-leading order in the holographic radial coordinate, for the case of spherical entangling surfaces. Using this new renormalization prescription, we directly find the C− function candidates for odd and even dimensional CFTs dual to Lovelock gravity. Our results illustrate the notable improvement that the Kounterterm method affords over other approaches, as it is non-perturbative and does not require that the Lovelock theory has limiting Einstein behavior.

We extend Maldacena’s argument, namely, obtaining Einstein gravity from Conformal Gravity, to six dimensional manifolds. The proof relies on a particular combination of conformal (and topological) invariants, which makes manifest the fact that 6D Conformal Gravity admits an Einstein sector. Then, by taking generalized Neumann boundary conditions, the Conformal Gravity action reduces to the renormalized Einstein-AdS action. These restrictions are implied by the vanishing of the traceless Ricci tensor, which is the defining property of any Einstein spacetime. The equivalence between Conformal and Einstein gravity renders trivial the Einstein solutions of 6D Critical Gravity at the bicritical point.

We derive a covariant expression for the renormalized holographic entanglement entropy for conformal field theories (CFTs) dual to quadratic curvature gravity in arbitrary dimensions. This expression is written as the sum of the bare entanglement entropy functional obtained using standard conical defect techniques, and a counterterm defined at the boundary of the extremal surface of the functional. The latter corresponds to the cod-2 self-replicating part of the extrinsic counterterms when evaluated on the replica orbifold. This renormalization method isolates the universal terms of the holographic entanglement entropy functional. We use it to compute the standard C-function candidate for CFTs of arbitrary dimension, and the type-B anomaly coefficient c for four-dimensional CFTs.

We study the holographic entanglement entropy of deformed entangling regions in three-dimensional CFTs dual to Einstein-AdS gravity, using a renormalization scheme based on the addition of extrinsic counterterms. In this prescription, when even-dimensional manifolds are considered, the universal contribution to the entanglement entropy is identified as the renormalized volume of the Ryu-Takayanagi hypersurface, which is written as the sum of a topological and a curvature term. It is shown that the change in the renormalized entanglement entropy due to the deformation of the entangling surface is encoded purely in the curvature contribution. In turn, as the topological part is given by the Euler characteristic of the Ryu-Takayanagi surface, it remains shape independent. Exploiting the covariant character of the extrinsic counterterms, we apply the renormalization scheme for the case of deformed entangling …

We show that the Kounterterms for pure AdS gravity in arbitrary even dimensions coincide with the boundary counterterms obtained through holographic renormalization if and only if the boundary Weyl tensor vanishes. In particular, the Kounterterms lead to a well posed variational problem for generic asymptotically locally AdS manifolds only in four dimensions. We determine the exact form of the counterterms for conformally flat boundaries and demonstrate that, in even dimensions, the Kounterterms take exactly the same form. This agreement can be understood as a consequence of Anderson’s theorem for the renormalized volume of conformally compact Einstein 4-manifolds and its higher dimensional generalizations by Albin and Chang, Qing and Yang. For odd dimensional asymptotically locally AdS manifolds with a conformally flat boundary, the Kounterterms coincide with the boundary counterterms except …