Topology sums, sectorwise holography, and horizon normalcy
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 α-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 dimℋBU=1 in consistent d>3 quantum gravity. If ℋBU is nontrivial, as in the Marolf--Maxfield formulation and in ensemble-like examples such as JT gravity, then HoI is naturally refined to an α-sectorwise statement, 𝒜∞(α)|0α⟩̅=ℋα, rather than completeness on the full topology-summed Hilbert space. In a fixed α-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 ℋBU to one dimension, the obstruction discussed here is absent.
Versions
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BibTeX
@misc{kumar2026topology,
title = {{Topology sums, sectorwise holography, and horizon normalcy}},
author = {Naman Kumar},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.20294},
eprint = {2605.20294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.20294},
}
RIS
TY - UNPB
TI - Topology sums, sectorwise holography, and horizon normalcy
AU - Naman Kumar
PY - 2026
DA - 2026/08/25
PB - arXiv
DO - 10.48550/arxiv.2605.20294
UR - https://arxiv.org/abs/2605.20294
AB - 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 α-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 dimℋ_BU=1 in consistent d>3 quantum gravity. If ℋ_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 α-sectorwise statement, 𝒜_∞^(α)|0_α⟩̅=ℋ_α, rather than completeness on the full topology-summed Hilbert space. In a fixed α-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 ℋ_BU to one dimension, the obstruction discussed here is absent.
ER -