Wormholes & Holography: An Introduction

We use the Einstein-Hilbert gravitational path integral to investigate gravitational entanglement at leading order O ⁡ ( 1 / G ) O(1/G) . We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies S n S_{n} are independent of n n at this order.

Abstract We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal “islands” in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the backreacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a sce …

We propose a solution of the naturalness problem in the context of the multiverse wavefunction without the anthropic argument. If we include microscopic wormhole configurations in the path integral, the wave function becomes a superposition of universes with various values of the coupling constants such as the cosmological constant, the parameters in the Higgs potential, and so on. We analyze the quantum state of the multiverse, and evaluate the density matrix of one universe. We show that the coupling constants induced by the wormholes are fixed in such a way that the density matrix is maximized. In particular, the cosmological constant, which is in general time-dependent, is chosen such that it takes an extremely small value in the far future. We also discuss the gauge hierarchy problem and the strong CP problem in this context. Our study predicts that the Higgs mass is mh = 140 ± 20 GeV and θ = 0.

By assuming that only (i) bi-local vertex operators which are diagonal with respect to the basis for local field operators, and (ii) the convergent elements with non-zero positive energy of the density matrix representing the quantum state of multiply connected wormholes, contribute the path integral that describes the effects of wormholes on ordinary matter fields at low energy, we obtain that the probability measure for multiply connected wormholes with non-degenerate energy spectrum is given in terms of a Planckian probability distribution for the momenta of a quantum field 1/2 alpha l 2 , where the alpha l s are the Coleman parameters, rather than a classical Gaussian distribution law; and that an observable classical universe can exist if and only if such multiply connected wormholes are allowed to occur.

We use the Einstein-Hilbert gravitational path integral to investigate gravitational entanglement at leading order O ⁡ ( 1 / G ) O(1/G) . We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies S n S_{n} are independent of n n at this order.