We investigate infrared dynamics of four-dimensional Einstein gravity in de Sitter space. We set up a general framework to investigate dynamical scaling relations in quantum/classical gravitational theories. The conformal mode dependence of Einstein gravity is renormalized to the extent that general covariance is not manifest. We point out that the introduction of an inflaton is necessary as a counterterm. We observe and postulate a duality between quantum effects in Einstein gravity and classical evolutions in an inflation (or quintessence) model. The effective action of Einstein gravity can be constructed as an inflation model with manifest general covariance. We show that $g=G_N H^2/π$: the only dimensionless coupling of the Hubble parameter $H^2$ and the Newton's coupling $G_N$ in Einstein gravity is screened by the infrared fluctuations of the conformal mode. We evaluate the one-loop $β$ function of $g$ with respect to the cosmic time $\log Ht$ as $β(g)=-(1/2)g^2$, i.e., $g$ is asymptotically free toward the future. The exact $β$ function with the backreaction of $g$ reveals the existence of the ultraviolet fixed point. It indicates that the de Sitter expansion stared at the Planck scale with a minimal entropy $S=2$. We have identified the de Sitter entropy $1/g$ with the von Neumann entropy of the conformal zero mode. The former evolves according to the screening of $g$ and the Gibbons-Hawking formula. The latter is found to increase by diffusion in the stochastic process at the horizon in a consistent way. Our Universe is located very close to the fixed point $g=0$ with a large entropy. We discuss possible physical implications of our results such as logarithmic decay of dark energy.
We employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H <…
Gravitational S-duality is defined by the contraction of two indices of the Riemann tensor with the epsilon tensor. We review its realization in linearized gravity, and study its generalization to full non-linear gravity by means of explicit examples: Up to a rescaling of the coordinates, it relates two Taub-NUT-Schwarzschild metrics by interchanging m with l, provided both parameters are non-zero. In the presence of a cosmological constant gravitational S-duality can be implemented at the expense of the introduction of a three-form field whose value turns out to be dual to the cosmological co…
In this paper we consider the critical gravity in four dimensional de Sitter space-time. We obtain logarithmic modes in the critical point of the theory. Then we show that these logarithmic modes in de Sitter space-time obey similar properties as the ones in AdS-space-time. Our result in this paper indicate that critical gravity theories in de Sitter space-times could lead to a de Sitter/log CFT correspondence.
We show that if Yang's model as the earliest TSR is completed, it should contain both Snyder's quantized space-time model as the earliest DSR, the de Sitter SR and their duality.
We derive a manifestly duality-invariant formulation of the action principle for linearized gravity on anti de Sitter background. The analysis is based on the two-potential formalism, obtained upon resolution of the constraints in the Hamiltonian formulation. We discuss the relevance of our result in the context of holography.
By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.
In this paper we study braneworld cosmology when the bulk space is a charged black hole in de Sitter space (Topological Reissner-Nordström de Sitter Space) in general dimension, then we compute leading order correction to the Friedmann equation that arise from logarithmic corrections to the entropy in the holographic-branworld cosmological framwork. Finally we consider the holographic entropy bounds in this senario, we show the entropy bounds are also modified by logarithmic term.
We calculate logarithmic corrections to the Bekenstein-Hawking entropy for three-dimensional BTZ black hole with J=0 and Kerr-de Sitter (KdS) space with J=0 including the Schwarzschild-de Sitter (SdS) solution due to thermal fluctuations. It is found that there is no distinction between the event horizon of the BTZ black hole and the cosmological horizon of KdS space. We obtain the same correction to the Cardy formula for BTZ, KdS, and SdS cases. We discuss AdS/CFT and dS/ECFT correspondences in connection with logarithmic corrections.
We perform the resummation of the infrared logarithms in the inflationary universe. Applying the renormalization group, we derive the stochastic equations as the effective theory at the horizon. We focus on the conformal zero mode to respect local Lorentz symmetry. Under Gaussian approximation, we derive the fundamental equation for the Universe (EqU). We also derive the identical equation from the first law of thermodynamics in a dual geometric picture. We believe it is a convincing evidence for de Sitter duality between quantum stochastic physics on the boundary and classical thermodynamics …
In this paper we compute leading order correction due to small statistical fluctuations around equilibrium, to the Cardy-Verlinde entropy formula (which is supposed to be an entropy formula of conformal field theory in any dimension) of a Topological Reissner-Nordstrom black hole in de Sitter space.
Gravitational instantons ''Lambda-instantons'' are defined here for any given value Lambda of the cosmological constant. A multiple of the Euler characteristic appears as an upper bound for the de Sitter action and as a lower bound for a family of quadratic actions. The de Sitter action itself is found to be equivalent to a simple and natural quadratic action. In this paper we also describe explicitly the reparameterization and duality invariances of gravity (in 4 dimensions) linearized about de Sitter space. A noncovariant doubling of the fields using the Hamiltonian formalism leads to first …
The higher-derivative $α'$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories featuring string-frame de Sitter vacua as solutions that are non-perturbative in $α'$, thus suggesting that classical string theory may realize de Sitter solutions in an unexpected fashion.
It is known that the graviton two-point function for the de Sitter invariant "Euclidean" vacuum in a physical gauge grows logarithmically with distance in spatially-flat de Sitter spacetime. We show that this logarithmic behaviour is a gauge artifact by explicitly demonstrating that the same behaviour can be reproduced by a pure-gauge two-point function.
We consider a self-interacting scalar field whose mass saturates the Breitenlohner-Freedman bound, minimally coupled to Einstein gravity with a negative cosmological constant in D \geq 3 dimensions. It is shown that the asymptotic behavior of the metric has a slower fall-off than that of pure gravity with a localized distribution of matter, due to the back-reaction of the scalar field, which has a logarithmic branch decreasing as r^{-(D-1)/2} ln r for large radius r. We find the asymptotic conditions on the fields which are invariant under the same symmetry group as pure gravity with negative …
In this paper a de Sitter Space version of Black Hole Complementarity is formulated which states that an observer in de Sitter Space describes the surrounding space as a sealed finite temperature cavity bounded by a horizon which allows no loss of information. We then discuss the implications of this for the existence of boundary correlators in the hypothesized dS/cft correspondence. We find that dS complementarity precludes the existence of the appropriate limits. We find that the limits exist only in approximations in which the entropy of the de Sitter Space is infinite. The reason that the …
It is shown that the addition of a topological invariant (Gauss-Bonnet term) to the anti-de Sitter (AdS) gravity action in four dimensions recovers the standard regularization given by holographic renormalization procedure. This crucial step makes possible the inclusion of an odd parity invariant (Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti) self-dual condition on the Weyl tensor. This argument allows to find the dual point of the theory where the holographic stress tensor is related to the boundary Cotton tensor as $T_{j}^{i}=\pm (\ell ^{2}/8πG)C_{j}^{i}$, which …
We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.
We study string loop corrections to the gravity kinetic terms in type IIB compactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of $D7$-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the $D7$-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kähler modu…
Hidden quantum-informatic symmetries of quasi-de Sitter backgrounds
Indian Statistical Institute（印度统计研究所）；University of Edinburgh（爱丁堡大学）；University of Sussex（萨塞克斯大学）；ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院、法国国家科学研究中心、巴黎文理研究大学、索邦大学、巴黎西岱大学）
We explicitly describe the last stages of black hole evaporation in the context of string theory : the combined study of Quantum Field Theory (QFT) and String Theory (ST) in curved backgrounds allows us to go further in the understanding of quantum gravity effects. The string ``analogue model''(or thermo-dynamical approach) is a well suited framework for this purpose.The results also apply to another physically relevant case: de Sitter background. Semiclassical (QFT) and quantum gravity (String) phases or regimes are properly determined (back reaction effects included). The Hawking-Gibbons tem…
It has been argued that the entropy of de Sitter space corresponds to the entanglement between disconnected regions computable by switching on a replica parameter $q$ modeled by the quotient dS$/\mathbb{Z}_q$. Within this framework, we show that the centrally-extended asymptotic symmetry algebra near the cosmic horizon is a single copy of the Virasoro algebra. The resulting density of states matches the semi-classical result of Gibbons and Hawking up to an undetermined constant that is chosen to reproduce the entanglement entropy previously found in the literature. It follows that the logarith…
T-Duality on a timelike circle does not interchange IIA and IIB string theories, but takes the IIA theory to a type $IIB^*$ theory and the IIB theory to a type $IIA^*$ theory. The type $II^*$ theories admit E-branes, which are the images of the type II D-branes under timelike T-duality and correspond to imposing Dirichlet boundary conditions in time as well as some of the spatial directions. The effective action describing an E$n$-brane is the $n$-dimensional Euclidean super-Yang-Mills theory obtained by dimensionally reducing 9+1 dimensional super-Yang-Mills on $9-n$ spatial dimensions and on…
We investigate gauge/gravity duality for gauge theories in de Sitter space. More precisely, we study a five-dimensional consistent truncation of type IIB supergravity, which encompasses a wide variety of gravity duals of strongly coupled gauge theories, including the Maldacena-Nunez solution and its walking deformations. We find several solutions of the 5d theory with dS_4 spacetime and nontrivial profiles for (some of) the scalars along the fifth (radial) direction. In the process, we prove that one of the equations of motion becomes dependent on the others, for nontrivial warp factor. This d…
In this paper we propose a holographic duality for classical gravity on a three-dimensional de Sitter space. We first show that a pair of SU$(2)$ Chern-Simons gauge theories reproduces the classical partition function of Einstein gravity on a Euclidean de Sitter space, namely $\mathbb{S}^3$, when we take the limit where the level $k$ approaches $-2$. This implies that the CFT dual of gravity on a de Sitter space at the leading semi-classical order is given by an SU$(2)$ Wess-Zumino-Witten (WZW) model in the large central charge limit $k\to -2$. We give another evidence for this in the light of…
Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only to the first few orders in the string scale $α'$. The functional renormalization group, in conjunction with the strong constraints imposed by T-duality, allows to derive cosmological effective actions to all orders in $α'$ while avoiding "truncations" of the theory space. We show that the resulting higher-derivative $α'$-corrections forbid the existence of de Sitter vacua, at least in regimes where string-loop corrections can be neglected. …
We consider 2+1 dimensional gravity with a cosmological constant, and explore a duality that exists between space-times that have the De Sitter group SO(3,1) as its local isometry group. In particular, the Lorentzian theory with a positive cosmological constant is dual to the Euclidean theory with a negative cosmological constant. We use this duality to construct a mapping between apparently unrelated space-times. More precisely, we exhibit a relation between the Euclidean BTZ family and some $T^2$-cosmological solutions, and between De-Sitter point particle space-times and the analytic contin…
Demanding $O(d,d)$-duality covariance, Hohm and Zwiebach have written down the action for the most general cosmology involving the metric, $b$-field and dilaton, to all orders in $α'$ in the string frame. Remarkably, for an FRW metric-dilaton ansatz the equations of motion turn out to be quite simple, except for the presence of an unknown function of a single variable. If this unknown function satisfies some simple properties, it allows de Sitter solutions in the string frame. In this note, we write down the Einstein frame analogues of these equations, and make some observations that make the …
Logarithmic corrections to near-extremal entropy of charged de Sitter black holes
Indian Institute of Technology Kanpur（坎普尔印度理工学院）；Pohang University of Science and Technology (POSTECH)（韩国科学技术院）；Asia Pacific Center for Theoretical Physics, POSTECH（韩国科学技术院亚太理论物理中心）；Seoul National University（首尔国立大学）
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.
In d=4 de Sitter space, novel conformally invariant photon-like theories consistently couple to charged matter. We show that these higher spin, maximal depth, partially massless systems enjoy a Maxwellian, "electric-magnetic" duality.
We study the general formulation of gauged supergravity in seven dimensions with sixteen supercharges keeping duality covariance by means of the embedding tensor formalism. We first classify all inequivalent duality orbits of consistent deformations. Secondly, we analyse the complete set of critical points in a systematic way. Interestingly, we find the first examples of stable de Sitter solutions within a theory with such a large amount of supersymmetry.
We investigate the physical measurability of the infrared instability of a de Sitter phase in the formalism recently proposed by Kitamoto et al.. We find that the logarithmic decay of the effective cosmological constant is only measurable if an additional clock field is introduced.
From the entropy argument for the dS swampland conjecture which connects the Gibbons-Hawking entropy bound with the distance conjecture, we find the entropic quasi-dS instability time given by $1/(\sqrt{ε_H}H)\log(m_{\rm Pl}/H)$ as the lifetime of quasi-dS spacetime. It depends on the slow-roll parameter, and contains the logarithmic factor $\log(m_{\rm Pl}/H)$ which can be found in the scrambling (or decoherence) time as well. Such a logarithmic factor enhances the geodesic distance of the modulus from the mere Planck scale, and also possibly relaxes the bound on $m_{\rm Pl}^2 \nabla^2 V/V$.
We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We consider self-interacting scalars of general mass, but focus especially on the massless and conformally coupled cases. We show that certain contributions grow logarithmically in conformal time both at tree and loop level. We also consider gauge fields and gravitons. The four-dimensional Fefferman-G…
The black hole information paradox is related to the area of event horizon, and potentially to the volume and singularity behind it. One example is the complexity/volume duality conjectured by Stanford and Susskind. Accepting the proposal of Christodoulou and Rovelli, we calculate the maximal volume inside regular black holes, which are free of curvature singularity, in asymptotically flat and anti-de Sitter spacetimes respectively. The complexity/volume duality is then applied to anti-de Sitter regular black holes. We also present an analytical expression for the maximal volume outside the de…
We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).
We establish a precise relation between mixed boundary conditions for scalar fields in asymptotically anti de Sitter spacetimes and the equation of state of the dual fluid. We provide a detailed derivation of the relation in the case of five bulk-dimensions for scalar fields saturating the Breitenlohner-Freedman bound. As a concrete example, we discuss the five dimensional scalar-tensor theories describing a constant speed of sound.
We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter $μ$ ($μ\neq0$). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower fall-off than the one relevant for General Relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generat…
We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the N…
We study the evolution of cosmological perturbations generated during de Sitter inflation in the singleton gravity theory. This theory is composed of a dipole ghost pair in addition to tensor. We obtain the singleton power spectra which show that the de Sitter/logarithmic conformal field theory (dS/LCFT) correspondence works for computing the power spectra in the superhorizon limit. Also we compute the spectral indices for light singleton which contains a logarithmic correction.
It has been proposed that a quantum group structure underlies de Sitter/Conformal field theory duality. These ideas are used to give a microscopic operator counting interpretation for the entropy of two-dimensional dilaton de Sitter space. This agrees with the Bekenstein-Hawking entropy up to a factor of order unity.
We present a class of dS/CFT correspondence between two-dimensional CFTs and three-dimensional de Sitter spaces. We argue that such a CFT includes an SU$(2)$ WZW model in the critical level limit $k\to -2$, which corresponds to the classical gravity limit. We can generalize this dS/CFT by considering the SU$(N)$ WZW model in the critical level limit $k\to -N$, dual to the higher-spin gravity on a three-dimensional de Sitter space. We confirm that under this proposed duality the classical partition function in the gravity side can be reproduced from CFT calculations. We also point out a duality…
In the semiclassical limit of de Sitter gravity a separation of scales takes place that divides the theory into a "cosmic" sector and a "microscopic" sector. A similar separation takes place in the double-scaled limit of SYK theory. We examine the scaling behaviors that accompany these limits and find parallels that support the previously conjectured duality between Jackiw-Teitelboim gravity (with positive cosmological constant), and double-scaled SYK. This paper is a companion to "dS JT Gravity and Double-Scaled SYK" by Adel Rahman, to appear simultaneously with this paper.
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are interchanged. This observation enables us to make a proposal in which supersymmetry is broken, but the four dimensional cosmological constant remains zero. An explicit model is proposed in which we calculate the cosmological constant. The phenomenology based on this model is presented, including the issue of the quark-lepton-Higgs mass matrix.
The well-known duality between quasinormal modes of any stationary, spherically symmetric and asymptotically flat or de Sitter black hole and parameters of the circular null geodesic was initially claimed for gravitational and test field perturbations. According to this duality the real and imaginary parts of the $\ell \gg n$ quasinormal mode (where $\ell$ and $n$ are multipole and overtone numbers respectively) are multiples of the frequency and instability timescale of the circular null geodesics respectively. Later it was shown that the duality is guaranteed only for test fields and may be …
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules by reducible ones obtained by requiring that only one of the two principal singular vectors of each module vanish. The resulting theory is then constructed systematically by repeatedly fusing these building block representations. This generates indecomposable representations of the type which signify the presence of logarithmic partner fields in the theory.…
We show that the $E-S \sim \log S$ behaviour found for long strings rotating on $AdS_5\times S^5$ may be reproduced by membranes rotating on $AdS_4\times S^7$ and on a warped $AdS_5$ M-theory solution. We go on to obtain rotating membrane configurations with the same $E-K \sim \log K$ relation on $G_2$ holonomy backgrounds that are dual to ${\mathcal{N}}=1$ gauge theories in four dimensions. We study membrane configurations on $G_2$ holonomy backgrounds systematically, finding various other Energy-Charge relations. We end with some comments about strings rotating on warped backgrounds.
We give an introductory review of gauge/gravity duality, and associated ideas of holography, emphasising the conceptual aspects. The opening Sections gather the ingredients, viz. anti-de Sitter spacetime, conformal field theory and string theory, that we need for presenting, in Section 5, the central and original example: Maldacena's AdS/CFT correspondence. Sections 6 and 7 develop the ideas of this example, also in applications to condensed matter systems, QCD, and hydrodynamics. Sections 8 and 9 discuss the possible extensions of holographic ideas to de Sitter spacetime and to black holes. S…
For a Hopf algebra B, we endow the Heisenberg double H(B^*) with the structure of a module algebra over the Drinfeld double D(B). Based on this property, we propose that H(B^*) is to be the counterpart of the algebra of fields on the quantum-group side of the Kazhdan--Lusztig duality between logarithmic conformal field theories and quantum groups. As an example, we work out the case where B is the Taft Hopf algebra related to the U_qsl(2) quantum group that is Kazhdan--Lusztig-dual to (p,1) logarithmic conformal models. The corresponding pair (D(B),H(B^*)) is "truncated" to (U_qsl(2),H_qsl(2))…
We review the construction of the unitary supermultiplets of the ${\cal{N}}=8$ d=5 anti-de Sitter (AdS_5) superalgebra SU(2,2|4), which is the symmetry group of the type IIB superstring theory on $AdS_5 \times S^5$, using the oscillator method.
We consider a brane universe in an asymptotically de Sitter background spacetime of arbitrary dimensionality. In particular, the bulk spacetime is described by a ``topological de Sitter'' solution, which has recently been investigated by Cai, Myung and Zhang. In the current study, we begin by showing that the brane evolution is described by Friedmann-like equations for radiative matter. Next, on the basis of the dS/CFT correspondence, we identify the thermodynamic properties of the brane universe. We then demonstrate that many (if not all) of the holographic aspects of analogous AdS-bulk scena…
This thesis consists of two parts. The first part deals with gauge/gravity duality in the context of anti de Sitter (AdS) spacetimes with de Sitter (dS) boundary, which can be used to study issues concerning strongly coupled field theory on de Sitter space, such as the issue of vacuum ambiguity. By calculating the symmetric two point function of the strongly coupled ${\cal N} = 4$ supersymmetric Yang-Mills theory on de Sitter space, we show that the vacuum ambiguity persists at strong coupling. Furthermore, the extra ambiguity in the strong coupling correlator seems to suggest that transition …
