Comments on wormholes, ensembles, and cosmology

TL;DR

This work investigates a holographic route to cosmology by embedding closed-universe spacetimes in AdS/CFT through analytic continuations of Euclidean wormholes. It analyzes the Black Hole Microstate Cosmology construction as a concrete realization where two decoupled CFTs couple to auxiliary degrees of freedom, yielding an ensemble-average description and a wavefunction of the universe in the auxiliary Hilbert space. The authors identify essential ingredients—auxiliary degrees of freedom, non-singlet gauge couplings, and spatially distributed auxiliary sectors—and propose generalizations to non-conformal theories and alternative geometries, linking ensemble averages to wormhole connectivity. They further discuss conceptual implications for the emergence of time, the role of Euclidean vs Lorentzian descriptions, and the interpretation of a time-symmetric quantum cosmology with multiple semiclassical branches.

Abstract

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.

Figures (6)

• Figure 1: The Maldacena-Maoz construction. Left: Euclidean AdS wormhole. Right: The analytic continuation to a closed universe big-bang / big-crunch cosmology.
• Figure 2: The Black Hole Microstate Cosmology (BHMC) construction. Left: A holographic CFT theory on a Euclidean cylinder with boundary degrees of freedom at the two ends is dual to a Euclidean spacetime with an end-of-the-world (ETW) brane having the geometry of a Euclidean wormhole. Right: In the associated Lorentzian geometry, the ETW brane lives behind a black hole horizon and has the geometry of a closed-universe big-bang/big-crunch cosmology. With many boundary degrees of freedom in the original picture, gravity can be localized to this ETW brane.
• Figure 3: Euclidean path integral construction for the state of a CFT on $S^d$ used in the BHMC construction. This is obtained from the standard path integral defining the vacuum state by truncating at some past Euclidean time $-\tau_0$ and choosing some boundary conditions there, with additional boundary degrees of freedom.
• Figure 4: Coupling the original CFTs to auxiliary degrees of freedom (a higher dimensional CFT on a cylinder in the BHMC case.) The partition function of the full theory is equal to the product of partition functions for the original theories averaged over an ensemble of sources defined using the path integral for the auxiliary degrees of freedom.
• Figure 5: Left: Schematic quiver diagram of two gauge initially decoupled gauge theory theories coupled to an auxiliary gauge theory via bifundamental matter. Center: D-brane construction of such a theory, with Dp-branes stretched between D(p+2)-branes and/or NS5 branes. The branes can be taken far apart at the same time as the decoupling limit so that the auxiliary degrees of freedom are spread over a finite extent in an extra dimension. Right: Geometry of the internal space for small $n/N$ in a conformal field theory example.