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

TL;DR

This paper tests the duality between double-scaled SYK and sine-dilaton gravity by computing one-loop quantum corrections, finding precise matches that support the proposed correspondence.

Contribution

It provides the first detailed one-loop correction calculations in sine-dilaton gravity and confirms the duality with double-scaled SYK at the quantum level.

Findings

Logarithmic correction to free energy matches between theories

Boundary correlator corrections agree precisely

Correct vacuum choice is crucial for accurate results

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.