Topology sums, sectorwise holography, and horizon normalcy

TL;DR

This paper explores how topology sums and sectorwise holography influence the holography of information in quantum gravity, revealing conditions under which horizons are smooth or firewalls may form.

Contribution

It introduces a refined perspective on holography of information considering baby-universe sectors and their impact on horizon normalcy and firewall arguments.

Findings

Sectorwise holography refines the holography of information principle.

A nontrivial baby-universe sector can obstruct firewall formation.

Local geometry alone may not determine horizon smoothness in sector-summed states.

Abstract

The ``holography of information'' (HoI) principle argues that gravity can encode information redundantly in asymptotic observables. Although HoI is ultimately a nonperturbative claim, its standard motivation uses semiclassical gravitational constraints, the boundary nature of the Hamiltonian, and vacuum-sector cyclicity. We ask what happens when the same semiclassical path-integral reasoning allows topology sums that generate baby-universe or $\alpha$-sector data. Our analysis is conditional: such sectors need not survive in every unitary completion, and the Baby Universe Hypothesis of McNamara and Vafa instead suggests $\dim\mathcal H_{\rm BU}=1$ in consistent $d>3$ quantum gravity. If $\mathcal H_{\rm BU}$ is nontrivial, as in the Marolf--Maxfield formulation and in ensemble-like examples such as JT gravity, then HoI is naturally refined to an $\alpha$-sectorwise statement, $\overline{\mathcal A_\infty^{(\alpha)}|0_\alpha\rangle}=\mathcal H_\alpha$, rather than completeness on the full topology-summed Hilbert space. In a fixed $\alpha$-sector, HoI may obstruct AMPS factorization and allow a smooth horizon; in an unconditioned topology-summed state, the sector-independent obstruction is not automatic. A Bell-pair diagnostic shows that a sector-independent smooth interior requires aligned interior reconstructions, or access to the sector label. Thus the HoI-based absence of firewalls becomes conditional on global sector data, in tension with the generally covariant expectation emphasized by Bousso that horizon normalcy should be determined by local semiclassical geometry. If the exact theory collapses $\mathcal H_{\rm BU}$ to one dimension, the obstruction discussed here is absent.