NONFACTORIZATION IN AdS₂ QUANTUM GRAVITY

Abstract

We study the phenomenon of nonfactorization in 1 + 1 dimensional quantum gravity through the lens of Jackiw-Teitelboim (JT) gravity and its dual construction as an SL(2, R)+ BF theory. After constructing the classical and quantum Hilbert space, we derive the Schwarzian boundary dynamics, interpreting their residual symmetries as underpinning boundary entanglement and nonfactorization. From the Euclidean path integral perspective, we note how nonfactorization manifests as contributions from connected bulk moduli to the topological expansion. In Lorentzian signature, we analyze nonfactorization via entanglement in the Thermofield Double state |TFD(β)⟩and discuss further the restrictions Lorentzian physics may impose on valid bulk moduli. Acknowledging these limitations, we outline a construction of the Saad–Shenker–Stanford matrix integral which realizes Euclidean JT gravity as dual to a nonperturbative, ensemble-averaged boundary theory. To clarify the role of the ensemble in resolving the chaotic dynamics of JT gravity, we develop a fine-grained construction of the JT path integral which incorporates the full spectra of Schwarzian dynamics. Our discussion refines the multiple mechanisms of chaos in JT gravity, though we stress the need for further nonperturbative developments to clarify the relationships between JT gravity, ensemble averaging, and quantum complexity.