Quantum gravity in the region very near horizon of an extreme Kerr black hole (whose angular momentum and mass are related by $J=G{M}^{2}$) is considered. It shown that consistent boundary conditions exist, for which asymptotic symmetry generators form one copy Virasoro algebra with central charge ${c}_{L}=\frac{12J}{\ensuremath{\hbar}}$. This implies near-horizon quantum states can be identified those (a chiral half of) a two-dimensional conformal field theory (CFT). Moreover, limit,...

The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between von Neumann entropy as calculated by Hawking and requirements of unitarity is fixed including new saddles gravitational path integral. These arise replica method complexified wormholes connecting different copies black hole. As number $n \to 1$, presence these leads island rule for computation fine-grained entropy. We discuss explicitly...

In this review, we describe recent progress on the black hole information problem that involves a new understanding of how to calculate entropy Hawking radiation. We show method for computing gravitational fine-grained entropy, developed over past 15 years, can be extended capture This technique reveals large corrections needed consistent with unitary evaporation.

Entanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law thermodynamics. In any CFT with semiclassical holographic dual, this has interpretation in dual gravitational theory as constraint on spacetimes to states. For small perturbations around vacuum state, we show that set such constraints for all ball-shaped spatial regions is exactly equivalent requirement geometry satisfy equations motion, linearized about pure AdS. theories entanglement...

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and spectrum Cardy regime, Δ ∞. We show that much stronger form of universality holds with large central charge c sparse light spectrum. In these theories, is at all values temperature, microscopic matches entropy for $$ \Delta \ge \frac{c}{6} . The same true three-dimensional quantum gravity; therefore our results provide simple necessary sufficient criteria 2d CFTs to behave...

Two-dimensional conformal field theories with a large central charge and small number of low-dimension operators are studied using the block expansion. A universal formula is derived for Renyi entropies N disjoint intervals in ground state, valid to all orders series This possible because full perturbative answer this regime comes from exchange stress tensor other descendants vacuum state. Therefore, entropy related Virasoro at charge. The entanglement entropy, computed by an analytic...

We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS4) is holographically dual to a three-dimensional conformal field (CFT3) living on the spacelike boundary dS4 at future timelike infinity. The CFT3 Euclidean Sp(N) vector model with anticommuting scalars. free flows under double-trace deformation an interacting IR. argue both CFTs are Vasiliev but different conditions bulk scalar field. Our analysis rests heavily analytic continuations and...

We consider the entanglement entropy in 2d conformal field theory a class of excited states produced by insertion heavy local operator. These include both high-energy eigenstates Hamiltonian and time-dependent quenches. compute universal contribution from stress tensor to single interval Renyi entropies entropy, conjecture that this dominates answer theories with large central charge sparse spectrum low-dimension operators. The resulting agree precisely holographic calculations...

Unitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting more than two dimensions, we show that this implies the averaged null energy, ∫ duT uu , must be non-negative. This non-local operator appears product expansion of local operators lightcone limit, and therefore contributes to n-point functions. We derive a sum rule isolates contribution is manifestly positive. The argument also applies certain...

A bstract We generalize the $$ T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation of CFT 2 to higher-dimensional large- N CFTs, and show that in holographic theories, resulting effective field theory matches semiclassical gravity AdS with a finite radial cutoff. also derive dual arbitrary bulk matter theories. Generally, deformations involve background fields as well operators. By...

Causality places nontrivial constraints on QFT in Lorentzian signature, for example fixing the signs of certain terms low energy Lagrangian. In d-dimensional conformal field theory, we show how such are encoded crossing symmetry Euclidean correlators, and derive analogous directly from bootstrap (analytically). The setup is a four-point function corresponding to propagation through shockwave. Crossing fixes log that appear block expansion, which constrains interactions low-lying operators....

A bstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged CFT. calculate averaged function and show that it can be reinterpreted as a sum topologies three This result leads us to conjecture CFT dimensions is holographically dual exotic theory three-dimensional gravity with U(1) c × symmetry composite boundary graviton. Additionally, for small central charge , we obtain general constraints on spectral...

A quantum extremal island suggests that a region of spacetime is encoded in the state another system, like encoding black hole interior Hawking radiation. We study conditions for islands to appear general spacetimes, with or without holes. They must violate Bekenstein's area bound precise sense, and boundary an satisfy several other information-theoretic inequalities. These combine impose very strong restrictions, which we apply cosmological models. find examples crunching universes. In...

A bstract The large- N limit of asymptotically flat two-dimensional dilaton gravity coupled to free matter fields provides a useful toy model for semiclassical black holes and the information paradox. Analyses asymptotic flux as given by entanglement entropy show that it follows Hawking curve, indicating is destroyed in these models. Recently, motivated developments AdS/CFT, island rule has been proposed. We define compute hole formation evaporation RST that, contrast, unitary Page curve....

Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in gravitational path integral, but for transient, holes most relevant to Hawking's paradox, these have not analyzed any detail. In this paper we study formed collapse Jackiw-Teitelboim gravity, and confirm that they lead island rule entropy. The main technical challenge is rely on a Euclidean while quantum hole exist only Lorentzian signature....

We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and U(1) current algebra. This differs from 2d conformal group, but some respects is equally powerful constraining theory. In particular, torus lead to modular covariance partition function, which used derive universal formula for asymptotic density states. For an application we turn holographic description...

We present a first-principles CFT calculation corresponding to the spherical collapse of shell matter in three dimensional quantum gravity. In field theory terms, we describe equilibration process, from early times thermalization, following sudden injection energy at time t = 0. By formulating continuum version Zamolodchikov's monodromy method calculate conformal blocks large central charge c, give framework compute general class probe observables state, incorporating full backreaction...

We investigate how entanglement spreads in time-dependent states of a 1+1 dimensional conformal field theory (CFT). The results depend qualitatively on the value central charge. In rational CFTs, which have charge below critical value, entropy behaves as if correlations were carried by free quasiparticles. This leads to long-term memory effects, such spikes mutual information widely separated regions at late times. When is above quasiparticle picture fails. Assuming no extended symmetry...

We study stress tensor correlation functions in four-dimensional conformal field theories with large N and a sparse spectrum. Theories this class are expected to have local holographic duals, so effective theory anti-de Sitter suggests that the sector should exhibit universal, gravity-like behavior. At linearized level, hallmark of locality emergent geometry is three-point 〈T T 〉, normally specified by three constants, approach universal structure controlled single parameter as gap higher...