A Third-Quantized Description of Spacetime Wormholes in AdS/CFT

Abstract

We propose an extension of AdS/CFT in which quantum gravitational wavefunctions of connected bulk geometries are assembled into a Fock space of universes. Splitting and joining interactions in a third-quantized Hamiltonian then provide a quantum description of changes in bulk connectivity and topology. Reduced phase-space quantization supplies the physical one-universe Hilbert space and a radial Schr\"odinger evolution with respect to which the topology-changing interactions are ordered. We develop the construction concretely in AdS$_3$ gravity with a torus boundary, where these ingredients can be described explicitly. The light spectrum is treated as fixed, non-normalizable background data, whereas the normalizable states above the black-hole threshold are quantized as dynamical modes. A conventional boundary theory is selected by choosing a coherent state whose universe-field expectation value, together with the fixed background contribution, yields consistent CFT data at the asymptotic boundary. Generic one-universe wavefunctions need not admit such an interpretation. This raises the possibility that CFT-realizable wavefunctions are nongeneric in the gravitational state space and are not closed under arbitrary superpositions of gravitational states. The known two-torus spacetime-wormhole amplitude, which lies at the heart of the factorization problem, provides concrete input for the topology-changing interactions of the third-quantized theory. A complementary cutting-and-gluing description yields an effective ensemble interpretation when the resulting gravitational sectors admit consistent boundary-theory interpretations, without assuming a fundamental ensemble of boundary theories. We also discuss replica wormholes and baby-universe processes within the same framework.