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 string’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).
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