Non-metricity approach to Jackiw-Teitelboim gravity

TL;DR

This paper formulates 2D Jackiw-Teitelboim gravity within symmetric teleparallel gravity using non-metricity tensors, identifying conditions for ghost-free scalar modes and constant curvature solutions.

Contribution

It introduces a novel non-metricity based formulation of 2D JT gravity, analyzing scalar mode propagation and ghost conditions in this framework.

Findings

A specific combination of non-metricity terms yields 2D JT gravity.

The conformal mode propagates as a scalar without ghosts.

Conditions for constant curvature solutions are established.

Abstract

We construct 2d Jackiw-Teitelboim (JT) gravity in the framework of symmetric teleparallel gravity based on a non-metricity tensor. In symmetric teleparallel gravity, we often use the scalar quantity $Q$ composed of the bilinear terms of the non-metricity tensor but $Q$ is not a unique scalar quantity from the viewpoint of covariance. However, other scalar quantities composed of the non-metricity tensor generate ghosts in general. In two dimensions, because a propagating gravitational mode does not exist, if we consider general scalar quantities, there might appear any propagating modes although these modes are often ghosts. We consider a general combination of the terms given by the bi-linear of the non-metricity tensors. After finding the condition that the conformal form of the metric is compatible with the coincident gauge, where connections vanish, we determine the combination so that a solution with constant curvature exists. The obtained model corresponds to 2d JT gravity in the framework of the symmetric teleparallel gravity. The conformal mode propagates as a scalar in this theory and we also consider the condition that the scalar mode is not a ghost.