We propose a consistent setup for the holographic dual of the strongly coupled large-Nc N=4 super Yang-Mills theory plasma which undergoes the Bjorken flow relevant to the quark-gluon plasma at BNL Relativistic Heavy Ion Collider and CERN LHC. The dual geometry is constructed order by order in a well-defined late-time expansion. The transport coefficients are determined by the regularity of the geometry. We prove, for the first time, that the dual geometry has an apparent horizon hence an event horizon, which covers a singularity at the origin. Further we prove that the dual geometry is regular to all orders in the late-time expansion under an appropriate choice of the transport coefficients. This choice is also shown to be unique. Our model serves as a concrete well-defined example of a time-dependent AdS/CFT dual.
Minkowski spacetime is transitive under ordinary translations, a transformation that do not have matrix representations. The de Sitter spacetime, on the other hand, is transitive under a combination of translations and proper conformal transformations, which do have a matrix representation. Such matrix, however, is not by itself a de Sitter generator: it gives rise to a conformal re-scaling of the metric, a transformation not belonging to the de Sitter group, and in general not associated with diffeomorphisms in spacetime. When dealing with variational principles and Noether's theorem in de Si…
The instability of (quasi) de Sitter spacetime from quantum gravitational effects has been discussed in many works. Especially, the gravitational backreaction from quantum energy momentum tensor is crucial for understanding the low-energy description of quantum gravity and sometimes destabilize the spacetime. In this paper we discuss the (quasi) de Sitter instability from gravitational backreaction involving quantum conformal anomaly. The conformal or trace anomaly corresponds to the quantum gravitational contributions of the massless conformal fields and affects the spacetime homogeneously. F…
We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic field in the de Sitter space from given currents and initial data. It only uses the Green's function of the massless Minkowskian scalar field. This leads to drastic simplifications in practical calculations. We apply this formula to the classical problem of the two charges of opposite signs at rest at the North and South Poles of the de Sitter space.
We show that the propagators of gravitons and scalar fields seen by a static patch observer in de Sitter spacetime are controlled by hidden SL(2,R) symmetries, at all frequencies. The retarded Green's function is determined by an SL(2,R) x SL(2,R) action generated by conformal Killing vectors of de Sitter spacetime times a line. This observation uses the fact that the static patch of dS_{d+1} x R is conformal to the hyperbolic patch of AdS_3 x S^{d-1}. The poles of the propagators, the quasinormal frequencies, are generated by associated SL(2,R) actions. The quasinormal mode generating algebra…
During inflation, the geometry of spacetime is described by a (quasi-)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group SO(1, 4) which acts like a conformal group on R^3: when the fluctuations are on super-Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three-dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides t…
We show how to generate non-trivial solutions to the conformally invariant, relativistic fluid dynamic equations by appealing to the Weyl covariance of the stress tensor. We use this technique to show that a recently studied solution of the relativistic conformally invariant Navier-Stokes equations in four-dimensional Minkowski space can be recast as a static flow in three-dimensional de Sitter space times a line. The simplicity of the de Sitter form of the flow enables us to consider several generalizations of it, including flows in other spacetime dimensions, second order viscous corrections…
The present work is the second part of a series of computations for the self-mass-squared of the conformally coupled (CC) scalar interacting with gravitons. This work includes the kinetic-kinetic and kinetic-conformal parts, and thus completes the full scalar self-mass squared at one loop order in de Sitter background when combined with the conformal-conformal part previously evaluated. We use dimensional regularization and renormalize the results by subtracting appropriate counterterms. The self-mass squared is finally ready to quantum-correct the CC scalar field equation so that one can stud…
In this paper, we study the conformally invariant field equations for vector-spinor field in de Sitter space-time. The solutions are also obtained in terms of the de Sitter-Dirac plane waves. The related two-point functions are calculated in both de Sitter ambient space formalism and intrinsic de Sitter coordinate. In order to study the conformal invariance, Dirac s six-cone formalism is utilized in which the field equations are expressed in a manifestly conformal way in 4 + 2 dimensional conformal space and then followed by the projection to de Sitter space.
The holographic dual of a gravitational theory around the de Sitter background is argued to be a Euclidean conformal gravity theory in one fewer dimensions. The measure for the holographic theory naturally includes a sum over topologies as well as conformal structures.
We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also clarify issues arising from the fact that both de Sitter and anti de Sitter have dual descriptions in terms of conformal field theory.
We consider classical and quantum strings in the conformally invariant background corresponding to the SL(2,R) WZWN model. This background is locally anti-de Sitter spacetime with non-vanishing torsion. Conformal invariance is expressed as the torsion being parallelized. The precise effect of the conformal invariance on the dynamics of both circular and generic classical strings is extracted. In particular, the conformal invariance gives rise to a repulsive interaction of the string with the background which precisely cancels the dominant attractive term arising from gravity. We perform both s…
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.
We describe how conformal Minkowski, dS- and AdS-spaces can be united into a single submanifold [N] of RP^5. It is the set of generators of the null cone in M^{2,4}. Conformal transformations on the Mink-, dS- and AdS-spaces are induced by O(2,4) linear transformations on M^{2,4}. We also describe how Weyl transformations and conformal transformations can be resulted in on [N]. In such a picture we give a description of how the conformal Mink-, dS- and AdS-spaces as well as [N] are mapped from one to another by conformal maps. This implies that a CFT in one space can be translated into a CFT i…
Constants of motion are calculated for 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2,3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.
The Riemann correlator with appropriately raised indices characterizes in a gauge-invariant way the quantum metric fluctuations around de Sitter spacetime including loop corrections from matter fields. Specializing to conformal fields and employing a method that selects the de Sitter-invariant vacuum in the Poincaré patch, we obtain the exact result for the Riemann correlator through order $H^4/m_\mathrm{p}^4$. The result is expressed in a manifestly de Sitter-invariant form in terms of maximally symmetric bitensors. Its behavior for both short and long distances (sub- and superhorizon scales)…
We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius `cavity' outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter…
Utilizing the conformal-flatness nature of 3-dim. Anti-de Sitter (AdS_3) black hole solution of Banados, Teitelboim and Zanelli, the quantisation of conformally-coupled scalar and spinor fields in this background spacetime is explicitly carried out. In particular, mode expansion forms and propagators of the fields are obtained in closed forms. The vacuum in this conformally-coupled field theories in AdS_3 black hole spacetime, which is conformally-flat, is the conformal vacuum which is unique and has global meaning. This point particularly suggests that now the particle production by AdS_3 bla…
We show that there is only one physically acceptable vacuum state for quantum fields in de Sitter space-time which is left invariant under the action of the de Sitter-Lorentz group $SO(1,d)$ and supply its physical interpretation in terms of the Poincare invariant quantum field theory (QFT) on one dimension higher Minkowski spacetime. We compute correlation functions of the generalized vertex operator $:e^{i\hat{S}(x)}:$, where $\hat{S}(x)$ is a massless scalar field, on the $d$-dimensional de Sitter space and demonstrate that their limiting values at timelike infinities on de Sitter space rep…
We show that far zone Mach and diffusion wake ``holograms'' produced by supersonic strings in anti--de Sitter space/conformal field theory (AdS/CFT) correspondence do not lead to observable conical angular correlations in the strict $N_c\to\infty$ supergravity limit if Cooper-Frye hadronization is assumed. However, a special {\em nonequilibrium} ``neck'' zone near the jet is shown to produce an apparent sonic boom azimuthal angle distribution that is roughly independent of the heavy quark's velocity. Our results indicate that a measurement of the dependence of the away-side correlations on the…
We evaluate one loop quantum gravity corrections to the conformally coupled (CC) scalar self-mass-squared on a locally de Sitter background. In this paper we consider only the conformal-conformal interaction part of the self-mass-squared. This complements the minimal-minimal part worked out in the previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007), arXiv: 0709.0536], and we will add the minimal-conformal part in a follow-up paper to complete the full self-mass-squared at one loop order. The computation is performed using dimensional regularization and the results are…
We exploit a recent computation of one graviton loop corrections to the self-mass [1] to quantum-correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the $R^2 ϕ^2$ counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.
We derive the leading quantum corrections to the gravitational potentials in a de Sitter background, due to the vacuum polarization from loops of conformal fields. Our results are valid for arbitrary conformal theories, even strongly interacting ones, and are expressed using the coefficients $b$ and $b'$ appearing in the trace anomaly. Apart from the de Sitter generalization of the known flat-space results, we find two additional contributions: one which depends on the finite coefficients of terms quadratic in the curvature appearing in the renormalized effective action, and one which grows lo…
We study the thermodynamics of de Sitter black holes with a conformally coupled scalar field. The geometry is that of the ``lukewarm'' Reissner-Nordstrom-de Sitter black holes, with the event and cosmological horizons at the same temperature. This means that the region between the event and cosmological horizons can form a regular Euclidean instanton. The entropy is modified by the non-minimal coupling of the scalar field to the geometry, but can still be derived from the Euclidean action, provided suitable modifications are made to deal with the electrically charged case. We use the first law…
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.
We briefly review the remarkable connections between light-front QCD, gravity in AdS space, and conformal quantum mechanics. We discuss, in particular, the group theoretical and geometrical aspects of the underlying one-dimensional quantum field theory. The resulting effective theory leads to a phenomenologically successful confining interaction potential in the relativistic light-front wave equation which incorporates relevant non-perturbative dynamical aspects of hadron physics.
We study the backreaction on the mean field geometry due to a non-conformal quantum field in a Robertson-Walker background. In the regime of small mass and small deviation from conformal coupling, we compute perturbatively the expectation value of the stress tensor of the field for a variety of vacuum states, and use it to obtain explicitly the semiclassical gravity solutions for isotropic perturbations around de Sitter spacetime, which is found to be stable. Our results show clearly the crucial role of the non-local terms that appear in the effective action: they cancel the contribution from …
A four-dimensional black hole solution of the Einstein equations with a positive cosmological constant, coupled to a conformal scalar field, is given. There is a curvature singularity at the origin, and scalar field diverges inside the event horizon. The electrically charged solution, which has a fixed charge-to-mass ratio is also found. The quartic self-interacting coupling becomes bounded in terms of Newton's and the cosmological constants.
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is conformally invariant and has two conformally invariant BRST operators. A curved space generalisation is found on any Riemannian 4-fold. This formulation has local Weyl invariance and two Weyl-invariant BRST symmetries, with an action and energy-momentum tensor that are BRST-exact. This theory is expected to have a holographic dual in 5-dimensional de Sitter space.
We show that a massive scalar field on a 2-dimensional Anti-De Sitter space can be mapped by means of a time-dependent canonical transformation into a massless free field theory when the mass square of the field is equal to minus the curvature of the background metric. We also provide the (hidden) conformal symmetry of the massive scalar field.
The energy-momentum tensor for a massless conformally coupled scalar field in de Sitter spacetime in the presence of a couple curved branes is investigated. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.
We have investigated the emerging conformal field theory behavior on the interior interface of the region near the cosmological event horizon on an example of massless Dirac fermions. Indeed, we have constructed and verified the emerging de Sitter/CFT correspondence for the near cosmological event horizon region. It is in this near horizon region where the infinitely thin shell of matter with the stiffest equation of state (Zeldovich's matter) is placed in the model for a thermodynamically stable `would be black hole' which is sometimes called a gravastar or a dark energy star. We put forward …
The higher-dimensional Kerr-NUT-de Sitter spacetime describes the general rotating asymptotically de Sitter black hole with NUT parameters. It is known that such a spacetime possesses a rank-2 closed conformal Killing-Yano (CKY) tensor as a ``hidden'' symmetry which provides the separation of variables for the geodesic equations and Klein-Gordon equations. We present a classification of higher-dimensional spacetimes admitting a rank-2 closed CKY tensor. This provides a generalization of the Kerr-NUT-de Sitter spacetime. In particular, we show that the Kerr-NUT-de Sitter spacetime is the only s…
We present the explicit global realization of the isometries of anti-de Sitter like spaces of signature $(d_-,d_+)$, and their algebras in the space of functions on the pseudo-Riemannian symmetric space $SO(d_- +1,d_+) / SO(d_-,d_+)$. The process of going to the invariant boundaries leads to the realization of the corresponding conformal groups and algebras. We compute systematically the geodesics in these spaces by considering the coset representation of them.
The Casimir forces on two parallel plates moving by uniform proper acceleration in static de Sitter background due to conformally coupled massless scalar field satisfying Dirichlet boundary conditions on the plates is investigated. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.
We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.
We use the AdS/CFT correspondence to calculate CFT correlation functions of vector and spinor fields. The connection between the AdS and boundary fields is properly treated via a Dirichlet boundary value problem.
We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as \textit{thermodynamic geometry}; (iv) the Poincaré method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first …
Scattering data can be generically described in terms of monodromies. Here we obtain scattering amplitudes for conformally coupled scalar fields in Kerr-de Sitter black holes using this monodromy technique. The only non-trivial parameter, the composite monodromy parameter $σ_{ij}$ between two regular singular points, can be solved implicitily in terms of the Painlevé VI $τ$-function. The application of the Virasoro conformal blocks to solve the latter can now be interpreted as a verification of the striking relationship between conformal symmetry and black holes.
We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary I^+ is deformed by the flux of gravitational radiation. We however impose an unconventional future "Dirichlet" boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at I^+. This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-…
Unitary principal series representations of the conformal group appear in the dS/CFT correspondence. These are infinite dimensional irreducible representations, without highest weights. In earlier work of Guijosa and the author it was shown for the case of two-dimensional de Sitter, there was a natural q-deformation of the conformal group, with q a root of unity, where the unitary principal series representations become finite-dimensional cyclic unitary representations. Formulating a version of the dS/CFT correspondence using these representations can lead to a description with a finite-dimens…
Perturbative quantum field theory in de Sitter space is known to give rise to a variety of contributions that diverge with time (secular terms). Despite significant progress, a complete understanding of the physical origin of these divergences remains an outstanding problem. In this paper, we will study the origin of secular divergences in de Sitter space for interacting theories that are near attractive conformal fixed points. We show that the secular divergences are determined by the anomalous dimensions of the same theory in flat space and can be re-summed using the dynamical renormalizatio…
We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The con…
In four lectures, delivered at the TASI 2010 summer school, I cover selected topics in the application of the gauge-string duality to nuclear and condensed matter physics. On the nuclear side, I focus on multiplicity estimates from trapped surfaces in AdS_5, and on the consequences of conformal symmetry for relativistic hydrodynamics. On the condensed matter side, I explain the fermion response to the zero-temperature limit of p-wave holographic superconductors.
The number of asymptotically de Sitter (non-singular) solutions of 5d dilatonic gravity with positive cosmological constant is found. These solutions are similar to the previously known asymptotically AdS spaces where dilaton may generate the singularity. Using these solutions the consistent $c$-function is proposed in the same way as in AdS/CFT. The consistency of RG flow gives further support for dS/CFT correspondence. From holographic RG flow equations we calculate the holographic 4d conformal anomaly with dilatonic contributions. This conformal anomaly turns out to be the same as in AdS/CF…
Recent work has uncovered a correspondence between theories in anti-de Sitter space, and those on its boundary. This has important implications for black holes in string theory which have near-horizon AdS geometries. Using the effective coupling to the boundary conformal field theory, I compute the low-energy, s-wave absorption cross-sections for a minimally coupled scalar in the near-extremal four- and five-dimensional black holes. The results agree precisely with semi-classical gravity calculations. Agreement for fixed scalars, and for the BTZ black hole, is also found.
We describe new non-supersymmetric conformal field theories in three and four dimensions, using the CFT/AdS correspondence. In order to believe in their existence at large N_c and strong 't Hooft coupling, we explicitly check the stability of the corresponding non-supersymmetric anti-de Sitter backgrounds. Cases of particular interest are the relevant deformations of the N=4 SCFT in SU(3) and SO(5) invariant directions. It turns out that the former is a stable, and the latter an unstable non-supersymmetric type IIB background.
As quotient spaces, Minkowski and de Sitter are fundamental, non-gravitational spacetimes for the construction of physical theories. When general relativity is constructed on a de Sitter spacetime, the usual Riemannian structure is replaced by a more general structure called de Sitter-Cartan geometry. In the contraction limit of an infinite cosmological term, the de Sitter-Cartan spacetime reduces to a singular, flat, conformal invariant four-dimensional cone spacetime, in which our ordinary notions of time interval and space distance are absent. It is shown that such spacetime satisfies all p…
We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point c…
For a pseudo-Riemannian manifold $X$ and a totally geodesic hypersurface $Y$, we consider the problem of constructing and classifying all linear differential operators $\mathcal{E}^i(X) \to \mathcal{E}^j(Y)$ between the spaces of differential forms that intertwine multiplier representations of the Lie algebra of conformal vector fields. Extending the recent results in the Riemannian setting by Kobayashi-Kubo-Pevzner [Lecture Notes in Math.~2170, (2016)], we construct such differential operators and give a classification of them in the pseudo-Riemannian setting where both $X$ and $Y$ are of con…
Motivated by holographic models of (pseudo)conformal Universe, we carry out complete analysis of linearized metric perturbations in the time-dependent two-brane setup of the Lykken-Randall type. We present the equations of motion for the scalar, vector and tensor perturbations and identify light modes in the spectrum, which are scalar radion and transverse-traceless graviton. We show that there are no other modes in the discrete part of the spectrum. We pay special attention to properties of light modes and show, in particular, that the radion has red power spectrum at late times, as anticipat…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) in semi-infinite space-time. In non-relativistic limit ($x\rightarrowεx, t\rightarrow t, ε\rightarrow 0$), boundary conformal algebra changes to boundary Galilean conformal algebra (BGCA). In this work, some aspects of AdS/BCFT in non-relatvistic limit were explored. We constrain correlation functions of Galilean conformal invariant fields with BGCA generators. For a situation with a boundary condition at surface $x=0$ ($z=\bar{z}$), our result is agree with non-relativistic limit of BCFT two-point function. We…
The de Sitter spacetime is transitive under a combination of translations and proper conformal transformations. Its usual family of geodesics, however, does not take into account this property. As a consequence, there are points in de Sitter spacetime which cannot be joined to each other by any one of these geodesics. By taking into account the appropriate transitivity properties in the variational principle, a new family of maximizing trajectories is obtained, whose members are able to connect any two points of the de Sitter spacetime. These geodesics introduce a new notion of motion, given b…
General relativity can be unambiguously formulated with Lorentz, de Sitter and anti-de Sitter tangent groups, which determine the fermionic representations. We show that besides of the Lorentz group only anti-de Sitter tangent group is consistent with all physical requirements.
By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry.
We construct a four dimensional de Sitter space upto a conformal transformation by compactifying the anisotropic SD3-brane solution of type IIB string theory on a six dimensional product space of the form $H_5 \times S^1$, where $H_5$ is a five dimensional hyperbolic space and $S^1$ is a circle. The radius of the hyperbolic space is chosen to be constant. The radius of the circle and the dilaton in four dimensions are time dependent and not constant in general. By different choices of parameters characterizing the SD3-brane solution either the dilaton or the radius of the circle can be made co…
We discuss several aspects of the proposed correspondence between quantum gravity on de Sitter spaces and Euclidean conformal field theories. The central charge appearing in the asymptotic symmetry algebra of three-dimensional de Sitter space is derived both from the conformal anomaly and the transformation law of the CFT stress tensor when going from dS_3 in planar coordinates to dS_3 with cosmological horizon. The two-point correlator for CFT operators coupling to bulk scalars is obtained in static coordinates, corresponding to a CFT on a cylinder. Correlation functions are also computed for…
