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Eternal Black Holes and Superselection in AdS/CFT

Donald Marolf, Aron C. Wall

TL;DR

This paper argues that Lorentzian wormholes in AdS/CFT imply superselection sectors in the bulk labeled by allowed wormhole connections, rather than a simple entangled multi-CFT dual. It demonstrates that a semiclassical interior forbids identifying a two-region wormhole with a pair of independent mono-asymptotic bulks, yielding bulk_2 ≅ (CFT)^2 × S_2 where S_2 encodes connectivity and is invisible to the boundary. Permutation symmetry considerations for multiple regions further constrain admissible sectors, enforcing either no wormholes or universal pairwise connectivity to preserve boundary statistics. The results illuminate how entanglement, locality, and horizon physics must be organized in holography and bear on questions about information transfer and firewall-like phenomena in multi-black-hole configurations.

Abstract

It has been argued i) that Lorentz-signature solutions with wormholes connecting n asymptotically AdS regions describe bulk quantum states dual to n entangled but non-interacting CFTs and ii) that such bulk wormhole states should be identified with similar entangled but non-interacting bulk systems, each describing quantum geometries with only a single asymptotic region. But if the wormhole is to behave semiclassically, we show that conjecture (ii) cannot hold. Instead, the theory of asymptotically AdS bulk quantum gravity must admit superselection sectors with respect to the CFT observables that are labeled by the type of wormhole connections allowed between black holes. Moreover, these superselection sectors are indistinguishable in the dual CFT. Finally, we describe restrictions on the possible superselection sectors associated with the spin-statistics relation and the expectation that black holes lying in distinct asymptotically AdS regions may be approximated by well-separated black holes in a single asymptotically AdS region.

Eternal Black Holes and Superselection in AdS/CFT

TL;DR

This paper argues that Lorentzian wormholes in AdS/CFT imply superselection sectors in the bulk labeled by allowed wormhole connections, rather than a simple entangled multi-CFT dual. It demonstrates that a semiclassical interior forbids identifying a two-region wormhole with a pair of independent mono-asymptotic bulks, yielding bulk_2 ≅ (CFT)^2 × S_2 where S_2 encodes connectivity and is invisible to the boundary. Permutation symmetry considerations for multiple regions further constrain admissible sectors, enforcing either no wormholes or universal pairwise connectivity to preserve boundary statistics. The results illuminate how entanglement, locality, and horizon physics must be organized in holography and bear on questions about information transfer and firewall-like phenomena in multi-black-hole configurations.

Abstract

It has been argued i) that Lorentz-signature solutions with wormholes connecting n asymptotically AdS regions describe bulk quantum states dual to n entangled but non-interacting CFTs and ii) that such bulk wormhole states should be identified with similar entangled but non-interacting bulk systems, each describing quantum geometries with only a single asymptotic region. But if the wormhole is to behave semiclassically, we show that conjecture (ii) cannot hold. Instead, the theory of asymptotically AdS bulk quantum gravity must admit superselection sectors with respect to the CFT observables that are labeled by the type of wormhole connections allowed between black holes. Moreover, these superselection sectors are indistinguishable in the dual CFT. Finally, we describe restrictions on the possible superselection sectors associated with the spin-statistics relation and the expectation that black holes lying in distinct asymptotically AdS regions may be approximated by well-separated black holes in a single asymptotically AdS region.

Paper Structure

This paper contains 7 sections, 9 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Eternal Black Hole
  3. A Puzzle with Multiple AdS regions
  4. Discussion
  5. Quantum Communication through a Wormhole
  6. No entanglement needed to meet a particular Bob.
  7. Entanglement needed to meet any Bob.

Figures (1)

  • Figure 1: A conformal diagram showing Alice and Bob created on the right and left boundaries, falling into the black hole, and meeting inside. The dotted lines are horizons.