Fully covariant determinant computation beyond minisuperspace in JT gravity

Develop a fully covariant computation of the functional determinant associated with the linearized constraint arising from integrating out the dilaton in Jackiw–Teitelboim gravity for fluctuations of the full spacetime metric g_{\mu\nu} (with appropriate gauge fixing), extending the minisuperspace analysis to verify consistency with the Schwarzian description.

Background

Throughout the paper the authors compute functional determinants and fixed-lapse propagators in minisuperspace JT gravity via the Gelfand–Yaglom theorem, confirming consistency and normalization. They note that extending these techniques beyond minisuperspace to the full spacetime metric g_{\mu\nu} is technically involved but important for connecting with the boundary Schwarzian theory.

Earlier in the introduction, they also remark that evaluating the determinant for full metric fluctuations is essential for verifying consistency with the Schwarzian description, indicating both the motivation and the technical difficulty of this extension, which they do not undertake here.

References

Finally, while the constrained expression eq:jt-amplitude introduced for \ac{jt} gravity is well-defined in minisuperspace, extending the determinant computation to fluctuations of the full spacetime metric $g_{\mu\nu}$ beyond minisuperspace requires a substantially more complicated analysis. We leave this fully covariant extension to future work.

— Functional Determinants for Constrained Path Integrals in Minisuperspace Jackiw-Teitelboim Gravity  (2512.21549 - Matsui, 25 Dec 2025) in Section 7 (Conclusion)