From black holes to baby universes in CGHS gravity

We study $\widehat{\text{CGHS}}$ gravity, a variant of the matterless Callan-Giddings-Harvey-Strominger model. We show that it describes a universal sector of the near horizon perturbations of non-extremal black holes in higher dimensions. In many respects this theory can be viewed as a flat space analog of Jackiw-Teitelboim gravity. The result for the Euclidean path integral implies that $\widehat{\text{CGHS}}$ is dual to a Gaussian ensemble that we describe in detail. The simplicity of this theory allows us to compute exact quantities such as the quenched free energy and provides a useful playground to study baby universes, averages and factorization. We also give evidence for the existence of a non-perturbative completion in terms of a matrix model. Finally, flat wormhole solutions are discussed.Comment: 55 pages, v2: minor changes, published versio

Lessons on Eternal Traversable Wormholes in AdS

We attempt to construct eternal traversable wormholes connecting two asymptotically AdS regions by introducing a static coupling between their dual CFTs. We prove that there are no semiclassical traversable wormholes with Poincar\'e invariance in the boundary directions in higher than two spacetime dimensions. We critically examine the possibility of evading our result by coupling a large number of bulk fields. Static, traversable wormholes with less symmetry may be possible, and could be constructed using the ingredients we develop here.Comment: 22 pages, 4 figures. v2: minor additions, matches published versio

Holography of information in de Sitter space

We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff-and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi's norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.Comment: 44 page

Gravitational perturbations from NHEK to Kerr

We revisit the spectrum of linear axisymmetric gravitational perturbations of the (near-)extreme Kerr black hole. Our aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. For the near horizon region of the (near-)extreme Kerr solution, i.e. the (near-)NHEK background, we provide a complete characterisation of axisymmetric modes. This involves an infinite tower of propagating modes together with the much subtler low-lying mode sectors that contain the deformations driving the black hole away from extremality. Our analysis includes their effects on the line element, their contributions to Iyer-Wald charges around the NHEK geometry, and how to reconstitute them as gravitational perturbations on Kerr. We present in detail how regularity conditions along the angular variables modify the dynamical properties of the low-lying sector, and in particular their role in the new developments of nearly-AdS$_2$ holography.Comment: 73 pages, 1 figure; v2: minor typos corrected; v3: matches published versio

The Hilbert space of de Sitter quantum gravity

We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity in an asymptotically de Sitter spacetime. Our solutions take the form of a universal phase factor multiplied by distinct diffeomorphism invariant functionals, with simple Weyl transformation properties, that obey the same Ward identities as a CFT partition function. The Euclidean vacuum corresponds to a specific choice of such a functional but other choices are equally valid. Each functional can be thought of as specifying a "theory" and, in this sense, the space of solutions is like "theory space". We describe another basis for the Hilbert space where all states are represented as excitations of the vacuum that have a specific constrained structure. This gives the finite $G_N$ generalization of the basis proposed by Higuchi in terms of group averaging, which we recover in the nongravitational limit.Comment: 47 page

Quantum information geometry of driven CFTs

Driven quantum systems exhibit a large variety of interesting and sometimes exotic phenomena. Of particular interest are driven conformal field theories (CFTs) which describe quantum many-body systems at criticality. In this paper, we develop both a spacetime and a quantum information geometry perspective on driven 2d CFTs. We show that for a large class of driving protocols the theories admit an alternative but equivalent formulation in terms of a CFT defined on a spacetime with a time-dependent metric. We prove this equivalence both in the operator formulation as well as in the path integral description of the theory. A complementary quantum information geometric perspective for driven 2d CFTs employs the so-called Bogoliubov-Kubo-Mori (BKM) metric, which is the counterpart of the Fisher metric of classical information theory, and which is obtained from a perturbative expansion of relative entropy. We compute the BKM metric for the universal sector of Virasoro excitations of a thermal state, which captures a large class of driving protocols, and find it to be a useful tool to classify and characterize different types of driving. For M\"obius driving by the SL(2,R) subgroup, the BKM metric becomes the hyperbolic metric on the unit disk. We show how the non-trivial dynamics of Floquet driven CFTs is encoded in the BKM geometry via M\"obius transformations. This allows us to identify ergodic and non-ergodic regimes in the driving. We also explain how holographic driven CFTs are dual to driven BTZ black holes with evolving horizons. The deformation of the black hole horizon towards and away from the asymptotic boundary provides a holographic understanding of heating and cooling in Floquet CFTs.Comment: 82 pages including references, 14 figure

Quantum hypothesis testing in many-body systems

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