A calculation of the Weyl anomaly for 6D Conformal Higher Spins

In this work we continue the study of the one-loop partition function for higher derivative conformal higher spin (CHS) fields in six dimensions and its holographic counterpart given by massless higher spin Fronsdal fields in seven dimensions. In going beyond the conformal class of the boundary round 6-sphere, we start by considering a Ricci-flat, but not conformally flat, boundary and the corresponding Poincar\'e-Einstein spacefilling metric. Here we are able to match the UV logarithmic divergence of the boundary with the IR logarithmic divergence of the bulk, very much like in the known 4D/5D setting, under the assumptions of factorization of the higher derivative CHS kinetic operator and WKB-exactness of the heat kernel of the dual bulk field. A key technical ingredient in this construction is the determination of the fourth heat kernel coefficient b6 for Lichnerowicz Laplacians on both 6D and 7D Einstein manifolds. These results allow to obtain, in addition to the already known type-A Weyl anomaly, two of the three independent type-B anomaly coefficients in terms of the third, say c_3 for instance. In order to gain access to c_3, and thus determine the four central charges independently, we further consider a generic non Ricci-flat Einstein boundary. However, in this case we find a mismatch between boundary and bulk computations for spins higher than two. We close by discussing the nature of this discrepancy and perspectives for a possible amendment.Comment: 13 page

One-loop divergences in 7D Einstein and 6D conformal gravities

Indexación: ScopusThe aim of this note is to unveil a striking equivalence between the one-loop divergences in 7D Einstein and 6D Conformal Gravities. The particular combination of 6D pointwise Weyl invariants of the 6D Conformal Gravity corresponds to that of Branson’s Q-curvature and can be written solely in terms of the Ricci tensor and its covariant derivatives. The quadratic metric fluctuations of this action, 6D Weyl graviton, are endowed with a sixth-order kinetic operator that happens to factorize on a 6D Einstein background into product of three shifted Lichnerowicz Laplacians. We exploit this feature to use standard heat kernel techniques and work out in one go the UV logarithmic divergences of the theory that contains in this case the four Weyl anomaly coefficients. In a seemingly unrelated computation, we determine the one-loop IR logarithmic divergences of 7D Einstein Gravity in a particular 7D Poincaré-Einstein background that is asymptotically hyperbolic and has the above 6D Einstein manifold at its conformal infinity or boundary. We show the full equivalence of both computations, as an outgrowth of the IR/UV connection in AdS/CFT correspondence, and in this way the time-honoured one-loop calculations in Einstein and higher-derivative gravities take an interesting new turn. © 2020, The Author(s)

Conserved charges for gravity with locally AdS asymptotics

A new formula for the conserved charges in 3+1 gravity for spacetimes with local AdS asymptotic geometry is proposed. It is shown that requiring the action to have an extremum for this class of asymptotia sets the boundary term that must be added to the Lagrangian as the Euler density with a fixed weight factor. The resulting action gives rise to the mass and angular momentum as Noether charges associated to the asymptotic Killing vectors without requiring specification of a reference background in order to have a convergent expression. A consequence of this definition is that any negative constant curvature spacetime has vanishing Noether charges. These results remain valid in the limit of vanishing cosmological constant.Comment: 5 pages, 2 Columns, revtex. Last version for Phys. Rev. Let

Black holes with topologically nontrivial AdS asymptotics

Asymptotically locally AdS black hole geometries of dimension d > 2 are studied for nontrivial topologies of the transverse section. These geometries are static solutions of a set of theories labeled by an integer 0 < k < [(d-1)/2] which possess a unique globally AdS vacuum. The transverse sections of these solutions are d-2 surfaces of constant curvature, allowing for different topological configurations. The thermodynamic analysis of these solutions reveals that the presence of a negative cosmological constant is essential to ensure the existence of stable equilibrium states. In addition, it is shown that these theories are holographically related to [(d-1)/2] different conformal field theories at the boundary.Comment: 13 Pages, 3 figures, two columns, Revtex, last version for PR

Analysing Charges in even dimensions

Lanczos-Lovelock theories of gravity, in its first order version, are studied on asymptotically locally anti de Sitter spaces. It is shown that thermodynamics satisfies the standard behavior and an expression for entropy is found for this formalism. Finally a short analysis of the algebra of conserved charges is displayed

Invariant conserved currents for gravity

We develop a general approach, based on the Lagrange-Noether machinery, to the definition of invariant conserved currents for gravity theories with general coordinate and local Lorentz symmetries. In this framework, every vector field \xi on spacetime generates, in any dimension n, for any Lagrangian of gravitational plus matter fields and for any (minimal or nonminimal) type of interaction, a current J[\xi] with the following properties: (1) the current (n-1)-form J[\xi] is constructed from the Lagrangian and the generalized field momenta, (2) it is conserved, d J[\xi] = 0, when the field equations are satisfied, (3) J[\xi]= d\Pi[\xi] "on shell", (4) the current J[\xi], the superpotential \Pi[\xi], and the charge Q[\xi] = \int J[\xi] are invariant under diffeomorphisms and the local Lorentz group. We present a compact derivation of the Noether currents associated with diffeomorphisms and apply the general method to compute the total energy and angular momentum of exact solutions in several physically interesting gravitational models.Comment: 15 pages, Revte

Determinant and Weyl anomaly of Dirac operator: a holographic derivation

We present a holographic formula relating functional determinants: the fermion determinant in the one-loop effective action of bulk spinors in an asymptotically locally AdS background, and the determinant of the two-point function of the dual operator at the conformal boundary. The formula originates from AdS/CFT heuristics that map a quantum contribution in the bulk partition function to a subleading large-N contribution in the boundary partition function. We use this holographic picture to address questions in spectral theory and conformal geometry. As an instance, we compute the type-A Weyl anomaly and the determinant of the iterated Dirac operator on round spheres, express the latter in terms of Barnes' multiple gamma function and gain insight into a conjecture by B\"ar and Schopka.Comment: 11 pages; new comments and references added, typos correcte

Quasinormal modes for the SdS black hole : an analytical approximation scheme

Quasinormal modes for scalar field perturbations of a Schwarzschild-de Sitter (SdS) black hole are investigated. An analytical approximation is proposed for the problem. The quasinormal modes are evaluated for this approximate model in the limit when black hole mass is much smaller than the radius of curvature of the spacetime. The model mirrors some striking features observed in numerical studies of time behaviour of scalar perturbations of the SdS black hole. In particular, it shows the presence of two sets of modes relevant at two different time scales, proportional to the surface gravities of the black hole and cosmological horizons respectively. These quasinormal modes are not complete - another feature observed in numerical studies. Refinements of this model to yield more accurate quantitative agreement with numerical studies are discussed. Further investigations of this model are outlined, which would provide a valuable insight into time behaviour of perturbations in the SdS spacetime.Comment: 12 pages, revtex, refs added and discussion expanded, version to appear in Phys. Rev.

Modeling Progressive Fibrosis with Pluripotent Stem Cells Identifies an Anti-fibrotic Small Molecule.

Progressive organ fibrosis accounts for one-third of all deaths worldwide, yet preclinical models that mimic the complex, progressive nature of the disease are lacking, and hence, there are no curative therapies. Progressive fibrosis across organs shares common cellular and molecular pathways involving chronic injury, inflammation, and aberrant repair resulting in deposition of extracellular matrix, organ remodeling, and ultimately organ failure. We describe the generation and characterization of an in&nbsp;vitro progressive fibrosis model that uses cell types derived from induced pluripotent stem cells. Our model produces endogenous activated transforming growth factor β (TGF-β) and contains activated fibroblastic aggregates that progressively increase in size and stiffness with activation of known fibrotic molecular and cellular changes. We used this model as a phenotypic drug discovery platform for modulators of fibrosis. We validated this platform by identifying a compound that promotes resolution of fibrosis in in&nbsp;vivo and ex&nbsp;vivo models of ocular and lung fibrosis