Comments on wormholes, ensembles, and cosmology

Certain closed-universe big-bang/big-crunch cosmological spacetimes may be obtained by analytic continuation from asymptotically AdS Euclidean wormholes, as emphasized by Maldacena and Maoz. We investigate how these Euclidean wormhole spacetimes and their associated cosmological physics might be described within the context of AdS/CFT. We point out that a holographic model for cosmology proposed recently in arXiv:1810.10601 can be understood as a specific example of this picture. Based on this example, we suggest key features that should be present in more general examples of this approach to cosmology. The basic picture is that we start with two non-interacting copies of a Euclidean holographic CFT associated with the asymptotic regions of the Euclidean wormhole and couple these to auxiliary degrees of freedom such that the original theories interact strongly in the IR but softly in the UV. The partition function for the full theory with the auxiliary degrees of freedom can be viewed as a product of partition functions for the original theories averaged over an ensemble of possible sources. The Lorentzian cosmological spacetime is encoded in a wavefunction of the universe that lives in the Hilbert space of the auxiliary degrees of freedom.

Higher spin wormholes from modular bootstrap

We investigate the connection between spacetime wormholes and ensemble averaging in the context of higher spin AdS3/CFT2. Using techniques from modular bootstrap combined with some holographic inputs, we evaluate the partition function of a Euclidean wormhole in AdS3 higher spin gravity. The fixed spin sectors of the dual CFT2 exhibit features that starkly go beyond conventional random matrix ensembles: power-law ramps in the spectral form factor and potentials with a double-well/crest underlying the level statistics.

Summing over geometries in string theory

We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on $$ {\mathrm{\mathcal{M}}}_3\times {\mathrm{S}}^3\times {\mathbbm{T}}^4 $$ ℳ 3 × S 3 × T 4 (with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). We strengthen the analysis of [1] and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ3. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕N SymN ($$ {\mathbbm{T}}^4 $$ T 4 ). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of $$ {\mathbbm{T}}^4 $$ T 4 and of deforming away from the orbifold by the marginal deformation.

VACUUM BRANS–DICKE THEORY AND WORMHOLES

This paper deals with vacuum Brans–Dicke theory in an anisotropic Kantowski–Sachs model and Euclidean wormhole solutions have been obtained. The Wheeler–Dewitt (WD) equation has been solved using separable form of the wave function and these solutions have been examined whether wormhole boundary condition due to Hawking is satisfied or not.

CREATION OF OPEN UNIVERSES AND CFT/AdS DUALITY

By replacing the singularity of the Hawking–Turok instanton for a regular asymptotically anti-de Sitter Euclidean wormhole, we conjecture that there may exist a holographic duality between CFT on the boundary of anti-de Sitter space and the Lorentzian isotropic open universes obtained by continuing the wormhole instanton according to the Hawking–Turok prescription.

BRANS–DICKE AND RELATED EUCLIDEAN WORMHOLES

In a recent paper1 Euclidean wormhole solution has been obtained with a vacuum Brans–Dicke theory with parameter ω=0. These wormholes suffer from unphysical values of the gravitational constant. One can relate the various known wormholes by means of conformal transformations; although one should not transform them directly to the Einstein frame as the gravitational constant there is "forced" physical: so removing the wormholes. However, by arguing for the existence of a fundamental minimum length scale such wormholes can now be considered as representative of quantum gravitational phenomena. One can also obtain wormholes as solutions of the quantum mechanical Wheeler–De Witt equation; now in Brans–Dicke for any ω>-3/2.