No abstract

We describe new boundary conditions for AdS2 in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to Diff(S1) ⋉ C∞(S1) whose breaking to SL(2, ℝ) × U(1) controls the near-AdS2 dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.

We compute the leading logarithmic correction to black hole entropy on the non-BPS branch of 4D N ≥ 2 supergravity theories. This branch corresponds to finite temperature black holes whose extremal limit does not preserve supersymmetry, such as the D0 − D6 system in string theory. Starting from a black hole in minimal Kaluza-Klein theory, we discuss in detail its embedding into N = 8, 6, 4, 2 supergravity, its spectrum of quadratic fluctuations in all these environments, and the resulting quantum corrections. We find that the c-anomaly vanishes only when N ≥ 6, in contrast to the BPS branch where c vanishes for all N ≥ 2. We briefly discuss potential repercussions this feature could have in a microscopic description of these black holes.

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 Poincaré 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.

We study gravitational perturbations around the near horizon geometry of the (near) extreme Kerr black hole. By considering a consistent truncation for the metric fluctuations, we obtain a solution to the linearized Einstein equations. The dynamics is governed by two master fields which, in the context of the nAdS_22/nCFT_11 correspondence, are both irrelevant operators of conformal dimension \Delta=2Δ=2. These fields control the departure from extremality by breaking the conformal symmetry of the near horizon region. One of the master fields is tied to large diffeomorphisms of the near horizon, with its equations of motion compatible with a Schwarzian effective action. The other field is essential for a consistent description of the geometry away from the horizon.

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice. These wavefunctionals must obey a set of constraints as a consequence of the diffeomorphism invariance of the theory, the most important of which is known as the Wheeler-DeWitt equation. We study these constraints perturbatively by expanding them to leading nontrivial order in Newton’s constant about a background AdS spacetime. We show that, even within perturbation theory, any wavefunctional that solves these constraints must have specific correlations between a component of the metric at infinity and energetic excitations of matter fields or transverse-traceless gravitons. These correlations disallow strictly localized excitations. We prove perturbatively that two states or two density matrices that coincide at the boundary for an infinitesimal interval of time must coincide everywhere in the bulk. This analysis establishes a perturbative version of holography for theories of gravity coupled to matter in AdS.

We study $$ \hat{\mathrm{CGHS}} $$ 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 $$ \hat{\mathrm{CGHS}} $$ 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. In particular we derive a “wormhole = diagonal” identity. We also give evidence for the existence of a non-perturbative completion in terms of a matrix model. Finally, flat wormhole solutions in this model are discussed.

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-AdS2 holography.