Abstract
We discuss all background charges and continuous consistent deformations of standard 2 d gravity theories with scalar matter fields. The background charges and those deformations which change nontrivially the gauge symmetries are closely linked, and exist only if the target space has a covariantly constant Killing vector (a null vector for the deformations). The deformed actions provide interesting novel 2 d gravity models. Some of them lead to non-critical string theories.
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