In the very low number of just 2 dimensions, quantum gravity is comparatively trivial and can be completely understood. While trivial as a theory of quantum gravity on a 2d spacetime, when that spacetime is regarded instead as the worldsheet of a string, then in fact the stringâ€™s worldsheet sigma-model theory is a theory of 2d quantum gravity (before the usual gravitational gauge fixing in 2d, which then makes what remains a conformal field theory, instead).

- Paul Ginsparg, Gregory Moore,
*Lectures on 2D gravity and 2D string theory (TASI 1992)*(arXiv:hep-th/9304011)

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