We consider the quantum mechanical description of the de Sitter static patch in three-dimensional general relativity. We consider a Lorentzian path integral that conjecturally computes the Fourier transform of the spectrum of the static patch Hamiltonian. We regulate a saddle point for this integral by a complex deformation that connects it to future infinity. Our computation is thus closely connected with the wave function of de Sitter gravity on a torus at future infinity. Motivated by this, we identify an infinite number of saddle points that contribute to our Lorentzian path integral. Their sum gives a surprisingly simple result, which agrees with the expected features of the de Sitter static patch. For example, the thermal entropy, evaluated at the de Sitter temperature, agrees with the Bekenstein-Hawking formula. We also obtain a spectrum in the spin-zero sector, which is bounded, discrete, and has an integer degeneracy of states. It includes a dense spectrum of states, making both positive and negative contributions to the trace, arranged in such a way that negative contributions are invisible in the computation of any smooth observable. Nevertheless, several mysteries remain.

Canada

Joydeep Chakravarty

United States

Alexander Maloney

Keivan Namjou

United Kingdom

Simon Ross

The spectrum of pure dS

Braneworlds inside an AdS black hole provide simple models where a closed cosmology can be encoded in a dual field theory. Previous studies have focused on pure-tension branes, where the only matter in the cosmology is that dual to the holographic bulk. We consider models with additional explicit matter fields on the brane. Both for perfect fluid matter and for an axion field on the brane, we show that this can avoid a self-intersection problem in the Euclidean construction of such geometries in higher dimensions.

Spain

José Barbón

Ayan Patra

Juan Pedraza

Cosmology inside a black hole: adding matter on the brane

We study multiparty entanglement signals, which are functions of a quantum state that are non-zero only when the state has multiparty entanglement. We consider known signals of three- and four-party entanglement, and propose new signals for four- and higher-party entanglement. We make some remarks on their general properties, but mainly focus on using holographic states in AdS /CFT as a test case to explore their properties. For both the AdS vacuum and multiboundary wormhole states, we find that the multiparty entanglement signals are generically non-zero and of order one in units of the central charge of the dual CFT, revealing substantial multiparty entanglement. In the large-horizon limit of multiboundary wormhole states, however, the signals for three or more parties become small, indicating the short-range nature of entanglement.

Belgium

Vijay Balasubramanian

Monica Kang

Chitraang Murdia

Signals of multiparty entanglement and holography

The double-cone geometry is a saddle of the gravitational path integral, which explains the chaotic statistics of the spectrum of black hole microstates. This geometry is the usual AdS-Schwarzschild black hole, but with a periodic identification of the time coordinate; the resulting singularity at the black hole horizon is regulated by making the geometry slightly complex. Here, we consider generalizations of the double-cone geometry which include the Lorentzian cosmology that sits between the event horizon and the black hole singularity. We analyze this in two and three dimensions, where the cosmology has compact spatial sections and big bang/crunch singularities. These singularities are regulated in the same way by slightly complexifying the metric. We show that this is possible while satisfying the Kontsevich-Segal criterion, implying that these geometries can be interpreted as perturbatively stable saddle points in general relativity. This procedure leads to a novel description of the cosmology in terms of standard observables in the dual boundary CFT. In three dimensions, the cosmological solution gives a new contribution to the two-point function of the density of states in the boundary CFT. Unlike the usual double cone, it describes correlations between black hole microstates with different masses, and in a limit describes correlations between the statistics of heavy states and states near the BTZ threshold.

A new observable for holographic cosmology

We consider soliton solutions in AdS4 with a flat slicing and Wilson loops around one cycle. We study the phase structure and find the ground state and identify supersymmetric solutions as a function of the Wilson loops. We work in the context of a scalar field truncation of gauged   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity, where all the dilatons are equal and all the axions vanish in the STU model. In this theory, we construct new soliton solutions parameterized by two Wilson lines. We find that there is a degeneracy of supersymmetric solutions. We also show that, for alternate boundary conditions, there exists a non-supersymmetric soliton solution with energy lower than the supersymmetric one.

Chile

Andrés Anabalón

Italy

Antonio Gallerati

Mario Trigiante

Supersymmetric solitons in gauged   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 8 supergravity

Models with closed FRW cosmologies on the worldvolume of a constant-tension brane inside a black hole provide an interesting setup for studying cosmology holographically. However, in more than two worldvolume dimensions, there are limitations on such models with flat spatial slices. I show that these limitations can be avoided by considering instead hyperbolic slices. This also naturally makes contact with previous work on Euclidean wormholes.

Cosmologies inside hyperbolic black holes

We discuss generalizations of the TFD to a density matrix on the doubled Hilbert space. We suggest that a semiclassical wormhole corresponds to a certain class of such density matrices, and specify how they are constructed. Different semi-classical profiles correspond to different non-overlapping density matrices. We show that this language allows for a finer criteria for when the wormhole is semiclassical, which goes beyond entanglement. Our main tool is the SYK model. We focus on the simplest class of such density matrices, in a scaling limit where the ER bridge is captured by chords going from one space to another, encoding correlations in the microscopic Hamiltonian. The length of the wormhole simply encodes the extent these correlations are eroded when flowing from one side to the other.

Israel

Micha Berkooz

Nadav Brukner

Masataka Watanabe

Going beyond ER=EPR in the SYK model

We study the construction of holographic models with closed FRW cosmologies on the worldvolume of a constant-tension brane inside a Schwarzschild-AdS black hole. In dimensions d &gt; 2, having a smooth Euclidean solution where the brane does not self-intersect limits the brane tension to T &lt; T *, preventing us from realising a separation of scales between the brane and bulk curvature scales. We show that adding interface branes to this model does not relax the condition on the brane tension.

Seamus Fallows

Constraints on cosmologies inside black holes

Switzerland

Günther Dissertori

Germany

Christian Caron

Editorial: Simon Eidelman (1948–2021)

We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system. We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components. The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them. In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state. We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.

Islands and mixed states in closed universes