De Sitter Boundary Research Articles

Stationary black holes and stars in the Brans-Dicke theory with Λ>0 revisited

It was shown a few years back that for a stationary regular black hole or star solution in the Brans-Dicke theory with a positive cosmological constant $\mathrm{\ensuremath{\Lambda}}$, endowed with a de Sitter or cosmological event horizon in the asymptotic region, not only there exists no nontrivial field configurations, but also the inverse Brans-Dicke parameter ${\ensuremath{\omega}}^{\ensuremath{-}1}$ must be vanishing. This essentially reduces the theory to Einstein's general relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $\ensuremath{\phi}$, couples directly to the $\mathrm{\ensuremath{\Lambda}}$-term in the energy-momentum tensor as well as $\mathrm{\ensuremath{\Lambda}}$ acts as a source in $\ensuremath{\phi}$'s equation of motion, it seems reasonable to ask: can $\ensuremath{\phi}$ become strong instead and screen the effect of $\mathrm{\ensuremath{\Lambda}}$, at very large scales, so that the asymptotic de Sitter structure is replaced by some alternative, yet still acceptable boundary condition? In this work we analytically argue that no such alternative exists, as long as the spacetime is assumed to be free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $\mathrm{\ensuremath{\Lambda}}$, irrespective of whether the asymptotic de Sitter boundary condition is imposed or not, a regular stationary black hole or even a star solution in the Brans-Dicke theory always necessitates ${\ensuremath{\omega}}^{\ensuremath{-}1}=0$, and thereby reducing the theory to general relativity. The qualitative differences of this result with that of the standard no hair theorems are also pointed out.

Yang-Mills model for centrally extended 2D gravity

A Yang-Mills theory linear in the scalar curvature for two-dimensional gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As compared with dilaton models, the role of the dilaton is played by the dual field strength of a $U(1)$ gauge field. All vacuum solutions are found. They are either black holes or have constant scalar curvature. Those with constant scalar curvature have constant dual field strength. In particular, solutions with vanishing cosmological constant but nonzero scalar curvature exist. In the conformal-Lorenz gauge, the model has a conformal field theory interpretation whose residual symmetry combines holomorphic diffeomorphisms with a subclass of $U(1)$ gauge transformations while preserving two-dimensional de Sitter and anti-de Sitter boundary conditions. This is the same symmetry as in Jackiw-Teitelboim-Maxwell gravity considered by Hartman and Strominger. It is argued that this is the only nontrivial Yang-Mills model linear in the scalar curvature that exists for real Lie algebras of dimension four.

Entropy of thermal CFTs on curved backgrounds

We use holography in order to study the entropy of thermal CFTs on (1+1)-dimensional curved backgrounds that contain horizons. Starting from the metric of the BTZ black hole, we perform explicit coordinate transformations that set the boundary metric in de Sitter or black-hole form. For a de Sitter boundary, the dual picture describes a CFT at a temperature different from that of the cosmological horizon. We determine minimal surfaces that allow us to compute the entanglement entropy of a boundary region, as well as the temperature affecting the energy associated with a probe quark on the boundary. For an entangling surface that coincides with the horizon, we study the relation between entanglement and gravitational entropy through an appropriate definition of the effective Newton's constant. We find that the leading contribution to the entropy is proportional to the horizon area, with a coefficient that accounts for the degrees of freedom of a CFT thermalized above the horizon temperature. We demonstrate the universality of our findings by considering the most general metric in a (2+1)-dimensional AdS bulk containing a non-rotating black hole and a static boundary with horizons.

Conformal scale factor inversion for domain walls and holography

We describe a correspondence between domain wall solutions of Einstein gravity with a single scalar field and self-interaction potential. The correspondence we call conformal scale factor inversion (CSFI) is a map comprising the inversion of the scale factor in conformal coordinates, and a transformation of the field and its potential which preserves the form of the Einstein equations for static and isotropic domain walls. By construction, CSFI maps the asymptotic anti--de Sitter boundary to the vicinity of a naked singularity in a theory with a special Liouville (exponential) scalar field potential; it is also a map in the parameter space of exponential potentials. The correspondence can be extended to linear fluctuations, being akin to an S-duality, and can be interpreted in terms of ``SUSY quantum mechanics'' for the fluctuation modes. The holographic implementation of CSFI relates the UV and IR regimes of a pair of holographic renormalization group flows; in particular, it is a symmetry of the GPPZ flow.

Entanglement entropy, horizons and holography

We study the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, using holography. We employ appropriate parametrizations of AdS space in order to obtain a Rindler or static de Sitter boundary metric. The holographic entanglement entropy for the regions enclosed by the horizons can be identified with the standard thermal entropy of these spaces. For this to hold, we define the effective Newton's constant appropriately and account for the way the AdS space is covered by the parametrizations.

Conformal extension of the Bunch-Davies state across the de Sitter boundary

In the setting of the massive Klein-Gordon equation on de Sitter space, we discuss Vasy’s asymptotic data at conformal infinity in terms of plane waves. In particular, we derive a short-hand formula for reconstructing solutions from their asymptotic data. Furthermore, we show that the natural Hadamard state induced from future (or past) conformal infinity coincides with the Bunch-Davies state.

Supersymmetric dS/CFT

We put forward new explicit realisations of dS/CFT that relate mathcal{N} = 2 supersymmetric Euclidean vector models with reversed spin-statistics in three dimensions to specific supersymmetric Vasiliev theories in four-dimensional de Sitter space. The partition function of the free supersymmetric vector model deformed by a range of low spin deformations that preserve supersymmetry appears to specify a well-defined wave function with asymptotic de Sitter boundary conditions in the bulk. In particular we find the wave function is globally peaked at undeformed de Sitter space, with a low amplitude for strong deformations. This suggests that supersymmetric de Sitter space is stable in higher-spin gravity and in particular free from ghosts. We speculate this is a limiting case of the de Sitter realizations in exotic string theories.

Complexity in de Sitter space

We consider the holographic complexity conjectures for de-Sitter invariant states in a quantum field theory on de Sitter space, dual to asymptotically anti-de Sitter geometries with de Sitter boundaries. The bulk holographic duals include solutions with or without a horizon. If we compute the complexity from the spatial volume, we find results consistent with general expectations, but the conjectured bound on the growth rate is not saturated. If we compute complexity from the action of the Wheeler–de Witt patch, we find qualitative differences from the volume calculation, with states of smaller energy having larger complexity than those of larger energy, even though the latter have bulk horizons.

HYM-flation: Yang–Mills cosmology with Horndeski coupling

We propose new mechanism for inflation using classical SU(2) Yang–Mills (YM) homogeneous and isotropic field non-minimally coupled to gravity via Horndeski prescription. This is the unique generally and gauge covariant ghost-free YM theory with the curvature-dependent action leading to second-order gravity and Yang–Mills field equations. We show that its solution space contains de Sitter boundary to which the trajectories are attracted for some finite time, ensuring the robust inflation with a graceful exit. The theory can be generalized to include the Higgs field leading to two-steps inflationary scenario, in which the Planck-scale YM-generated inflation naturally prepares the desired initial conditions for the GUT-scale Higgs inflation.

Holographic thermalization in Gauss-Bonnet gravity with de Sitter boundary

We introduce higher-derivative Gauss-Bonnet correction terms in the gravity sector and we relate the modified gravity theory in the bulk to the strongly coupled quantum field theory on a de Sitter boundary. We study the process of holographic thermalization by examining three nonlocal observables, the two-point function, the Wilson loop and the holographic entanglement entropy. We study the time evolution of these three observables and we find that as the strength of the Gauss-Bonnet coupling is increased, the saturation time of the thermalization process to reach thermal equilibrium becomes shorter with the dominant effect given by the holographic entanglement entropy.

Holographic gravitational infall in the hard wall model

An infalling shell in the hard wall model provides a simple holographic model for energy injection in a confining gauge theory. Depending on its parameters, a scalar shell either collapses into a large black brane, or scatters between the hard wall and the anti--de Sitter boundary. In the scattering regime, we find numerical solutions that keep oscillating for as long as we have followed their evolution, and we provide an analytic argument that shows that a black brane can never be formed. This provides examples of states in infinite-volume field theory that never thermalize. We find that the field theory expectation value of a scalar operator keeps oscillating, with an amplitude that undergoes modulation.

Conformal Gravity Holography in Four Dimensions

We formulate four-dimensional conformal gravity with (anti-)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown-York stress tensor, the other is a "partially massless response". The on shell action and response functions are finite and do not require holographic renormalization. Finally, we discuss phenomenologically interesting examples, including the most general spherically symmetric solutions and rotating black hole solutions with partially massless hair.

How to construct a gravitating quantum electron star

Motivated by the holographic study of Fermi surfaces, we develop methods to solve Einstein gravity coupled to fermions and gauge fields, with anti--de Sitter boundary conditions and a chemical potential.

Holographic horizons

We examine how the $(2+1)$-dimensional anti-de Sitter space is covered by the Fefferman-Graham system of coordinates for Minkowski, Rindler, and static de Sitter boundary metrics. We show that, in the last two cases, the coordinates do not cover the full anti-de Sitter space. On a constant-time slice, the line delimiting the excluded region has endpoints at the locations of the horizons of the boundary metric. Its length, after an appropriate regularization, reproduces the entropy of the dual conformal field theory on the boundary background. The horizon can be interpreted as the holographic image of the line segment delimiting the excluded region in the vicinity of the boundary.

Real time response ondS3: the topological AdS black hole and the bubble

We study real time correlators in strongly coupled = 4 supersymmetric Yang-Mills theory on dS3 ? S1, with antiperiodic boundary conditions for fermions on the circle. When the circle radius is larger than a critical value, the dual geometry is the so-called ``topological AdS5 black hole''. Applying the Son-Starinets recipe in this background we compute retarded glueball propagators which exhibit an infinite set of poles yielding the quasinormal frequencies of the topological black hole. The imaginary parts of the propagators exhibit thermal effects associated with the Gibbons-Hawking temperature due to the cosmological horizon of the de Sitter boundary. We also obtain R-current correlators and find that after accounting for a small subtlety, the Son-Starinets prescription yields the retarded Green's functions. The correlators do not display diffusive behaviour at late times. Below the critical value of the circle radius, the topological black hole decays to the AdS5 ``bubble of nothing''. Using a high frequency WKB approximation, we show that glueball correlators in this phase exhibit poles on the real axis. The tunnelling from the black hole to the bubble is interpreted as a hadronization transition.

Superconducting loop quantum gravity and the cosmological constant

We argue that the cosmological constant is exponentially suppressed in a candidate ground state of loop quantum gravity as a nonperturbative effect of a holographic Fermi-liquid theory living on a two-dimensional spacetime. Ashtekar connection components, corresponding to degenerate gravitational configurations breaking large gauge invariance and CP symmetry, behave as composite fermions that condense as in Bardeen–Cooper–Schrieffer theory of superconductivity. Cooper pairs admit a description as wormholes on a de Sitter boundary.

Coupled bulk and brane fields about a de Sitter brane

We consider the evolution of a bulk scalar field in anti-de Sitter (AdS) spacetime linearly coupled to a scalar field on a de Sitter boundary brane. We present results of a spectral analysis of the system, and find that the model can exhibit both bound and continuum resonant modes. We find that zero, one, or two bound states may exist, depending upon the masses of the brane and bulk fields relative to the Hubble length and the AdS curvature scale and the coupling strength. In all cases, we find a critical coupling above which there exists a tachyonic bound state. We show how the 5-dimensional spectral results can be interpreted in terms of a 4-dimensional effective theory for the bound states. We find excellent agreement between our analytic results and the results of a new numerical code developed to model the evolution of bulk fields coupled to degrees of freedom on a moving brane. This code can be used to model the behavior of brane-world cosmological perturbations in scenarios for which no analytic results are known.

Creating Naked Singularities and Negative Energy

A brief review is given of three recent results concerning classical solutions of gravitational theories: (1) With asymptotically anti de Sitter boundary conditions, there are matter theories satisfying the positive energy theorem which violate cosmic censorship. (2) Despite supersymmetry, there are solutions to \U0001d4a9 = 8 supergravity in which the total gravitational energy is arbitrarily negative. This theory can also violate cosmic censorship. (3) A large class of supersymmetric compactifications (including all simply connected Calabi–Yau manifolds) have solutions with negative four dimensional effective energy density.

Static black holes with a negative cosmological constant: Deformed horizon and anti–de Sitter boundaries

Using perturbative techniques, we investigate the existence and properties of a static solution for the Einstein equation with a negative cosmological constant, which we call the deformed black hole. We derive a solution for a static and axisymmetric perturbation of the Schwarzschild--anti-de Sitter black hole that is regular in the range from the horizon to spacelike infinity. The key result is that this perturbation simultaneously deforms the two boundary surfaces---i.e., both the horizon and spacelike two-surface at infinity. Then we discuss the Abbott-Deser mass and the Ashtekar-Magnon one for the deformed black hole, and according to the Ashtekar-Magnon definition, we construct the thermodynamic first law of the deformed black hole. The first law has a correction term which can be interpreted as the work term that is necessary for the deformation of the boundary surfaces. Because the work term is negative, the horizon area of the deformed black hole becomes larger than that of the Schwarzschild--anti-de Sitter black hole, if compared under the same mass, indicating that the quasistatic deformation of the Schwarzschild--anti-de Sitter black hole may be compatible with the thermodynamic second law (i.e., the area theorem).

QCD and dimensional deconstruction

Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an ``open moose.'' Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\infty}$ the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics, such as vector meson dominance. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a ``cosh'' metric interpolating between two anti--de Sitter (AdS) boundaries. For the pion form factor, the single pole \ensuremath{\rho}-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/conformal field theory-like prescription emerges in the computation of current-current correlators. We speculate on the role of the model in the theory dual to QCD.