ON HIGHER-DERIVATIVE DILATONIC GRAVITY IN 2 DIMENSIONS

We discuss lowering the order of the two-dimensional scalar-tensor R(2 ) quantum gravity, by mapping the most general version of the model to a multi-dilaton gravity, which is essentially the sigma-model coupled with the Jackiw-Teitelboim-like gravity. In the continuation of our p revious research, we calculate the divergent part of the one-loop effe ctive action in a 2-D scalar-tensor (dilatonic) gravity with the R(2)- term, which belongs to a specific degenerate case and cannot be obtain ed from the general expression. The corresponding finiteness condition s are found.