Explicit realization of bulk ER=EPR

Construct an explicit realization of the bulk ER=EPR correspondence by demonstrating, within a bulk gravitational theory, a concrete equivalence between the Lorentzian two-sided black hole geometry prepared by the Hartle–Hawking state and an entangled sum over single-sided geometries obtained by factorizing that state.

Background

The essay discusses a Lorentzian interpretation of a shrinkability condition for Euclidean path integrals in gravity, which relates an unfactorized Hartle–Hawking state evolving into a two-sided black hole to a factorized Hartle–Hawking state evolving into an entangled sum over single-sided geometries. This is presented as the bulk counterpart of the boundary ER=EPR equivalence between the two-sided black hole and the thermal field double state.

Realizing this bulk equivalence requires a complete set of spacetime-ending defects (entanglement branes) that implement bulk factorization consistently. While arguments and indications are given for their necessity (e.g., connections to the cobordism conjecture), the essay notes that an explicit construction realizing the bulk ER=EPR correspondence has not yet been achieved.