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On tests for baby universes in AdS/CFT

Kenneth Higginbotham

TL;DR

This paper addresses the Antonini–Rath puzzle by relaxing the assumption of a single isometric holographic map in AdS/CFT. By introducing two holographic maps, $V_{nb}$ for the no-baby bulk and $V_{baby}$ for the baby-bulk (the latter using post-selection on the baby universe), it shows that the boundary swap operator $\mathcal{S}_{\partial}$ has two bulk duals, $\mathcal{S}$ and $\mathcal{S}_{\mathrm{baby}}$, with $\langle\mathcal{S}_{\partial}\rangle = \langle\mathcal{S}\rangle_{nb} = \langle\mathcal{S}_{\mathrm{baby}}\rangle_{baby}$. The explicit qubit model reinforces that the non-perturbative bulk operator correctly reproduces boundary expectations, while the naive perturbative operator does not. The analysis reveals regimes where $\mathcal{S}_{\partial}$ cannot distinguish between the two pictures, especially when an external reference $R$ is entangled with the boundary, suggesting semiclassical baby universes can be viable in those regimes. Finally, the work discusses incorporating observers into the holographic maps, which can yield nontrivial operators on the baby universe and potentially offer further criteria to resolve the AR puzzle, with the caveat that distinguishing the two bulk states may depend on the observer construction and remains open for future work.

Abstract

To address a puzzle by Antonini and Rath -- where a single CFT state has two bulk duals, one with a baby universe and one without -- Engelhardt and Gesteau recently devised a test for baby universes in AdS/CFT. Using the extrapolate dictionary, they showed that the boundary dual of a bulk swap test favored bulk spacetimes without a baby universe, providing evidence against their semiclassical validity. However, recent work suggests that holographic maps should post-select on such closed universes, and we argue that this is consistent with the extrapolate dictionary. We therefore construct a new holographic map for bulk states with baby universes and use this to show that the swap test cannot distinguish between Antonini and Rath's two candidate bulk duals. This not only allows for a valid semiclassical description of the baby universe, but also enables the application of recent techniques for including observers in holographic maps.

On tests for baby universes in AdS/CFT

TL;DR

This paper addresses the Antonini–Rath puzzle by relaxing the assumption of a single isometric holographic map in AdS/CFT. By introducing two holographic maps, for the no-baby bulk and for the baby-bulk (the latter using post-selection on the baby universe), it shows that the boundary swap operator has two bulk duals, and , with . The explicit qubit model reinforces that the non-perturbative bulk operator correctly reproduces boundary expectations, while the naive perturbative operator does not. The analysis reveals regimes where cannot distinguish between the two pictures, especially when an external reference is entangled with the boundary, suggesting semiclassical baby universes can be viable in those regimes. Finally, the work discusses incorporating observers into the holographic maps, which can yield nontrivial operators on the baby universe and potentially offer further criteria to resolve the AR puzzle, with the caveat that distinguishing the two bulk states may depend on the observer construction and remains open for future work.

Abstract

To address a puzzle by Antonini and Rath -- where a single CFT state has two bulk duals, one with a baby universe and one without -- Engelhardt and Gesteau recently devised a test for baby universes in AdS/CFT. Using the extrapolate dictionary, they showed that the boundary dual of a bulk swap test favored bulk spacetimes without a baby universe, providing evidence against their semiclassical validity. However, recent work suggests that holographic maps should post-select on such closed universes, and we argue that this is consistent with the extrapolate dictionary. We therefore construct a new holographic map for bulk states with baby universes and use this to show that the swap test cannot distinguish between Antonini and Rath's two candidate bulk duals. This not only allows for a valid semiclassical description of the baby universe, but also enables the application of recent techniques for including observers in holographic maps.

Paper Structure

This paper contains 5 sections, 23 equations, 1 figure.

Table of Contents

  1. Introduction
  2. A tale of two holographic maps
  3. Simplicity of $\mathcal{S}_\partial$
  4. Including observers
  5. Concluding remarks

Figures (1)

  • Figure 1: A graphical representation of the no-baby state $\psi^{(\mathop{\mathrm{nb}}\nolimits)}$ (top) and baby state $\psi^{(\mathop{\mathrm{baby}}\nolimits)}$ (bottom). The red discs labeled ($a$, $b$) represent AdS spacetimes with asymptotic boundaries ($A$, $B$). The blue ball labeled $i$ represents a baby (or closed) universe.