Inequivalence of First and Second Order Formulations in D=2 Gravity Models

The usual equivalence between the Palatini and metric (or affinity and vielbein) formulations of Einstein theory fails in two spacetime dimensions for its “Kaluza–Klein” reduced (as well as for its standard) version. Among the differences is the necessary vanishing of the cosmological constant in the first order forms. The purely affine Eddington formulation of Einstein theory also fails here.