Poisson-sigma model for 2D gravity with non-metricity

We present a Poisson-sigma model describing general 2D dilaton gravity with non-metricity, torsion and curvature. It involves three arbitrary functions of the dilaton field, two of which are well known from metric compatible theories, while the third one characterizes the local strength of non-metricity. As an example we show that α' corrections in 2D string theory can generate (target space) non-metricity. (fast track communication)