(Generalized) Conformal Quantum Mechanics of 0-Branes and Two-Dimensional Dilaton Gravity

We study the relation between the (generalized) conformal quantum mechanics of 0branes and the two-dimensional dilaton gravity. The two-dimensional actions obtained from the supergravity effective actions for the (dilatonic) 0-branes through the compactification on a sphere are related to known two-dimensional dilaton gravity models. The SL(2,R) symmetry of the (generalized) conformal quantum mechanics is realized within such two-dimensional models. The two-dimensional dilatonic gravity model derived from the non-dilatonic 0-brane action is related to the Liouville theory and therefore is conformal, whereas the two-dimensional model derived from the dilatonic 0-brane action does not have the conformal symmetry. CERN-TH/99-295 September, 1999