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arXiv · 2410.20747

Non-metricity approach to Jackiw-Teitelboim gravity

Shin'ichi Nojiri·S. D. Odintsov
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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.

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Shin'ichi Nojiri, S. D. Odintsov. 2025-02-28. Non-metricity approach to Jackiw-Teitelboim gravity. https://arxiv.org/abs/2410.20747

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