Sine-dilaton gravity vs double-scaled SYK: exploring one-loop quantum corrections

TL;DR

This work tests the proposed duality between double-scaled SYK and 2d sine-dilaton gravity by performing a detailed one-loop path-integral analysis. It computes the logarithmic correction to the gravity free energy and the one-loop correction to a bulk matter bilocal observable, finding agreement with DSSYK up to a simple ordering ambiguity, and highlights the crucial role of the Hartle-Hawking vacuum boundary conditions. The authors encode sine-dilaton gravity via a deformed Schwarzian (the q-Schwarzian) and apply a generalized Gel'fand–Yaglom approach to evaluate the one-loop determinant, ensuring a consistent matching with the DSSYK transfer-matrix structure. They also derive the gravity-side one-loop correction to the boundary-to-boundary propagator of a non-minimally coupled matter field and demonstrate exact correspondence with the DSSYK result, strengthening the holographic picture beyond the JT limit. Overall, the results provide nontrivial evidence for the DSSYK–sine-dilaton duality and offer a concrete framework for incorporating quantum corrections in this setting, with potential implications for understanding bulk UV completions and cosmological (de Sitter) aspects of DSSYK.

Abstract

We provide non-trivial checks of the recently proposed duality between double-scaled SYK and a 2d dilaton gravity model with sine potential, studying the path integral at one-loop level. Specifically, we compute the logarithmic correction to the free energy of sine-dilaton gravity and, up to potential ordering ambiguities, we find a match with the corresponding quantity in double-scaled SYK. The computation relies on the description of sine-dilaton gravity in terms of a version of the q-Schwarzian theory, the quantum deformation of the standard Schwarzian model dual to JT gravity. A crucial aspect of the calculation is selecting the correct Hartle-Hawking vacuum for the gravitational theory, which implies a specific choice of boundary conditions for the one-loop determinant, computed using a generalization of the Gel'fand-Yaglom's theorem. We also evaluate the gravitational one-loop correction to the boundary to boundary propagator of a non-minimally coupled matter field in the bulk theory, showing a perfect agreement with the corresponding quantum correction of matter correlators in double-scaled SYK.