Further Evidence Against a Semiclassical Baby Universe in AdS/CFT

TL;DR

This work tackles whether semiclassical baby universes can arise in AdS/CFT, focusing on the Antonini–Rath puzzle. It constructs an $O(1)$-complexity boundary observable $\mathcal{S}_{\partial}$, derived from the extrapolate dictionary and causal-wedge encoding, that distinguishes bulk descriptions with and without a semiclassical baby universe. The analysis shows that, under the extrapolate dictionary and isometric causal-wedge encoding, a semiclassical baby universe is incompatible unless the baby-universe Hilbert space is one-dimensional, effectively selecting the no-baby-universe bulk as the correct dual. The argument extends to broader states without nontrivial QESs, indicating a general obstruction to semiclassical baby universes within AdS/CFT for a wide class of geometries.

Abstract

We argue that a large class of asymptotically AdS geometries with a semiclassical baby universe cannot be realized within the AdS/CFT correspondence. This in particular resolves a recent puzzle introduced by Antonini and Rath, in which a single CFT state appeared to simultaneously describe an AdS spacetime with a baby universe and one without. We construct a low-energy (and low complexity) boundary operator whose expectation values in the descriptions with and without the baby universe cannot match if the baby universe is semiclassical. This operator conclusively identifies the actual bulk dual: the spacetime without a semiclassical baby universe. This result assumes only that AdS/CFT admits an extrapolate dictionary and an asymptotically isometric encoding of the causal wedge into the dual CFT, without which the correspondence may well be vacuous.

Figures (3)

• Figure 1: Ref. AntSas23's path integral preparation of the baby universe, as used by AR in their presentation of the puzzle. There are two asymptotic boundaries $A$ and $B$ at different temperatures, both below Hawking-Page, and a heavy operator insertion ${\cal O}$ in Euclidean time. In Lorentzian time there are three disconnected bulk regions: $a,i,b$.
• Figure 2: The action of the swap operator ${ \cal S}$ on the semiclassical states $\psi^{(1)}\otimes \psi^{(1)}$ (left panel) and $\psi^{(2)}\otimes \psi^{(2)}$ (right panel). This figure represents a time slice of the doubled semiclassical geometries. In both cases the original boundary system is the red system, and the doubled system is the blue system. On the left panel, ${\cal S}$ swaps $ab$ with $a^\prime b^\prime$, but not$i$ with $i^\prime$. On the right panel, there is no closed universe so ${\cal S}$ swaps the whole bulk $ab$ with the whole bulk $a^\prime b^\prime$.
• Figure 3: The state $\left| \Psi \right\rangle_{A}={\cal O}_{1}{\cal O}_{2}\left| \Psi^{(c)} \right\rangle_{A}$. Turning off the sources removes the event horizon.