Open-channel quantization of JT gravity at finite cutoff

Abstract

Direct canonical quantization of Jackiw--Teitelboim gravity at finite cutoff leads to a critically singular Pöschl--Teller problem whose endpoint admits inequivalent self-adjoint domains. We solve the full one-parameter family, obtain its exact spectral data, and identify the extension parameter with a renormalized short-distance matching datum in geodesic-length space. Self-adjointness, positivity, and unitary Brown--York evolution leave a stable family, whereas a source-free local completion without an endpoint contact term selects the Friedrichs realization. With the Brown--York clock and a local cap prescription fixed, the disk amplitude distinguishes the domains. In the large-boundary limit the bulk operator becomes universally Liouville, while a cap tied to the receding endpoint can retain domain dependence. Analytic continuation also maps radial resonances to poles of the Brown--York resolvent. These results isolate the short-distance datum that distinguishes the reduced canonical realizations and that a microscopic completion would have to determine.

22 pages