Baby Universes in AdS$_3$

TL;DR

This paper explores Euclidean geometries in AdS$_3$ with baby universes, showing they are typically subdominant and encoded in suppressed wave function components, but can be made dominant leading to mixed CFT states.

Contribution

It introduces a method to make baby universe geometries the leading saddle, revealing their impact on the dual CFT state and providing insights into their semi-classical stability.

Findings

Baby universes are generally subdominant in AdS$_3$ geometries.

Applying a specific prescription makes baby universe geometries dominant.

Fluctuations in baby universes are small, ensuring semi-classical reliability.

Abstract

We discuss Euclidean geometries in AdS$_3$ whose Lorentzian slicing gives rise to closed baby universes with a spatial geometry given by genus $g\geq 2$ surfaces. Our setup only involves a two-dimensional holographic CFT defined on a higher genus Riemann surface and thus provides a well-posed alternative to shell states whose microscopic duals are less well understood. We find that geometries giving rise to baby universes are always subdominant. It follows that the baby universe does not provide a semi-classical description of the state since it is encoded in an exponentially suppressed part of the wave function. We then apply a prescription developed in \cite{Belin:2025wju} to make the baby universe geometry the leading saddle. In the process, the CFT state becomes mixed, in agreement with the qualitative gravitational picture. We show that the fluctuations in the baby universe are small, even at fixed central charge, making the geometry reliable in the semi-classical limit. Finally, we discuss the interpretation of this mixed state in pure gravity from the perspective of the Virasoro TQFT.