Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS_2 rather than AdS_2.
The Goheer-Kleban-Susskind no-go theorem says that the symmetry of de Sitter space is incompatible with finite entropy. The meaning and consequences of the theorem are discussed in the light of recent developments in holography and gravitational path integrals. The relation between the GKS theorem, Boltzmann fluctuations, wormholes, and exponentially suppressed non-perturbative phenomena suggests: the classical symmetry between different static patches is broken; and that eternal de Sitter space -- if it exists at all -- is an ensemble average.
Effective dynamics and quantum information in de Sitter wedge holography
University of Science and Technology of China（中国科学技术大学）；Peng Huanwu Center for Fundamental Theory（彭桓武理论研究中心）；Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立学院）
The holographic entanglement entropy is computed for an entangling surface that coincides with the horizon of a boundary de Sitter metric. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. The entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. The entanglement entropy takes the expected form of the de Sitter entropy, incl…
Bulk reconstruction formulas similar to HKLL are obtained for de Sitter and anti-de Sitter spaces as the inverse Gel'fand Graev Radon transform. While these generalize our previous result on the Euclidean anti-de Sitter space, their validity in here is restricted only to odd dimensions in both instances. The exact Wightman function for the de Sitter space is then derived analytically. The GGR transform fixes the coefficient of the Wightman function. For the anti-de Sitter space it is shown that a reconstruction formula exists for the case of time-like boundary as well. The restriction on the d…
Carroll Geometry Meets De Sitter Space via Holography
Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Center of Gravity, The Niels Bohr Institute, Copenhagen University（哥本哈根大学尼尔斯·玻尔研究所引力中心）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院与斯德哥尔摩大学）
We propose an explicitly calculable example of holography on 3-dimensional de Sitter space by providing a prescription to analytic continue a higher-spin holography on 3-dimensional anti-de Sitter space. Applying the de Sitter holography, we explicitly compute bulk correlation functions on 3-dimensional de Sitter space at late time in a higher-spin gravity. These expressions are consistent with recent analysis based on bulk Feynman diagrams. Our explicit computations reveal how holographic computations could provide fruitful information.
We consider the AdS/dS CFT correspondence and study the nature of the thermal bath of the de Sitter field theory using holography. Unlike the temperature of a thermal field theory in flat spacetime, the temperature of a superconformal field theory on de Sitter space is an integral part of the theory and leaves intact the conformal symmetry and supersymmetry. In the dual AdS side, there is no black hole. Instead we have cosmological expansion of the de Sitter factor. We consider a number of different observables, such as the entanglement entropy, two point correlation function, Wilson loops cor…
We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d+1 dimensions involves two coupled CFT sectors constrained by residual d-dimensional gravity. In the d=2 case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large central charge and a sparse …
We give a group-theoretic interpretation of relativistic holography as equivalence between representations of the anti de Sitter algebra describing bulk fields and boundary fields. Our main result is the explicit construction of the boundary-to-bulk operators for arbitrary integer spin the framework of representation theory. Further we show that these operators and the bulk-to-boundary operators are intertwining operators. In analogy to the de Sitter case, we show that each bulk field has two boundary (shadow) fields with conjugated conformal weights. These fields are related by another intert…
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…
In the setting of non-interacting Klein-Gordon fields on asymptotically anti-de Sitter spacetimes, we show that algebras of observables localized in a neighborhood of the boundary are subalgebras of a boundary algebra. The underlying mechanism is directly related to holography for classical fields. In particular, the proof relies on unique continuation theorems at the conformal boundary.
We study extremal surfaces in the Schwarzschild de Sitter spacetime with real mass parameter. We find codim-2 timelike extremal surfaces stretching between the future and past boundaries that pass through the vicinity of the cosmological horizon in a certain limit. These are analogous to the surfaces in arXiv:1711.01107 [hep-th]. We also find spacelike surfaces that never reach the future/past boundaries but stretch indefinitely through the extended Penrose diagram, passing through the vicinity of the cosmological and Schwarzschild horizons in a certain limit. Further, these exhibit interestin…
We calculate 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.
It is shown that the correspondence principle and the holographic principle are incompatible in the background of an eternal Schwarzschild-anti-de Sitter geometry. The argument is based on the observation that algebraic structures of local quantum field and CFT operators are not equivalent. This implies, in particular, the bulk CFT must be singular near the black-hole horizon. A CFT Hilbert space representation is elaborated which may correspond to the AdS black hole in the dual theory.
The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordstr$\ddot{o}$m anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordstr$\ddot{o}$m anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function $f$ at their final states. It is found that both of the near-extremal and extremal …
Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the first part of this paper the Ryu-Takayanagi prescription, the theory of fast scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be "hyperfast." In…
In this thesis Chern-Simons theories based on Lie algebras with invariant metric are constructed. It is discussed how contractions lead systematically to (higher spin) kinematical algebras of, e.g., Poincaré, Galilei and Carroll type and how they can be extended to permit an invariant metric. A new generalization of the Inönü-Wigner contractions explains why the invariant metric stays nondegenerate in the ultra-relativistic limes to the Carroll algebras. Since asymptotic symmetries give a first glance of possible dual theories consistent boundary conditions for Lifshitz and null-warped higher …
We develop further the codim-2 future-past extremal surfaces stretching between the future and past boundaries in de Sitter space, discussed in previous work. We first make more elaborate the construction of such surfaces anchored at more general subregions of the future boundary, and stretching to equivalent subregions at the past boundary. These top-bottom symmetric future-past extremal surfaces cannot penetrate beyond a certain limiting surface in the Northern/Southern diamond regions: the boundary subregions become the whole boundary for this limiting surface. For multiple disjoint subregi…
Holography in flipped AdS/$\mathbb{Z}$: Another approach to dS holography
Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术研究院、物理科学与技术学院）；School of Physics, Peking University（北京大学物理学院）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
We compute the spectrum of extremal nonBPS black holes in four dimensions by studying supergravity on their AdS$_2\times S^2$ near horizon geometry. We find that the spectrum exhibits significant simplifications even though supersymmetry is completely broken. We interpret our results in the framework of nAdS$_2$/nCFT$_1$ correspondence and by comparing with dimensional reduction from AdS$_3$/CFT$_2$ duality. As an additional test we compute quantum corrections to extremal black hole entropy on the nonBPS branch and recover results previously determined using very different methods.
A class of invariant states under de Sitter isometries is constructed in d-dimensional Conformal Field Theories from the universal sector of AdS/CFT dualities. These states extend the Mottola-Allen $α$-vacua to theories containing scalar primary operators of arbitrary scaling dimensions, and are proven to explicitly break conformal symmetry. Two-point correlators in these states are shown to satisfy a generalized spectral decomposition in terms of free massive propagators. It is also pointed out that the spectral decomposition of generic Euclidean correlators is known in the mathematics litera…
Built on our observation that entangling surfaces of the boundary field theory are great co-dimension one spheres in the context of DS/dS correspondence, we study some information theoretic quantities of the field theory dual intensively using holographic proposals. We will focus on entanglement entropy (EE), entanglement of purification (EoP) and complexity. Several fundamental observations and analysis are provided. For EE, we focus on its scaling behavior, which indicates the nature of the relevant degrees of freedom. Moreover, we find that EE provides us with important information of the e…
We study 4-dimensional Schwarzschild de Sitter black holes in the regime where the black hole mass is small compared with the de Sitter scale. Then the de Sitter temperature is very low compared with that of the black hole and we study the black hole, approximating the ambient de Sitter space as a frozen classical background. We consider distant observers in the static diamond, far from the black hole but within the cosmological horizon. Using 2-dimensional tools, we find that the entanglement entropy of radiation exhibits linear growth in time, indicative of the information paradox for the bl…
We interpret cosmological evolution holographically as a renormalisation group flow in a dual Euclidean field theory, as suggested by the conjectured dS/CFT correspondence. Inflation is described by perturbing around the infra-red fixed point of the dual field theory. The spectrum of the cosmic microwave background radiation is determined in terms of scaling violations in the field theory. The dark energy allows similar, albeit less predictive, considerations. We discuss the cosmological fine-tuning problems from the holographic perspective.
We study extremal surfaces in the static patch coordinatization of de Sitter space, focussing on the future and past universes. We find connected timelike codim-2 surfaces on a boundary Euclidean time slice stretching from the future boundary $I^+$ to the past boundary $I^-$. In a limit, these surfaces pass through the bifurcation region and have minimal area with a divergent piece alone, whose coefficient is de Sitter entropy in 4-dimensions. These are reminiscent of rotated versions of certain surfaces in the $AdS$ black hole. We close with some speculations on a possible $dS/CFT$ interpreta…
We conjecture that, in asymptotically anti-de Sitter space, two solutions of the Wheeler-DeWitt equation that coincide asymptotically must also coincide in the bulk. This suggests that the essential elements of holography are already present in canonical gravity. Our argument sheds light on why holography works only in gravitational theories, and also on the significance of anti-de Sitter boundary conditions.
