AN EINSTEIN-HILBERT ACTION FOR AXI-DILATON GRAVITY IN 4-DIMENSIONS

We examine the axi-dilatonic sector of low-energy string theory and de monstrate how the gravitational interactions involving the axion and d ilaton fields may be derived from a geometrical action principle invol ving the curvature scalar associated with a non-Riemannian connection. In this geometry the antisymmetric tenser 3-form field determines the torsion of the connection on the frame bundle while the gradient of t he metric is determined by the dilaton field. By expressing the theory in terms of the Levi-Civita connection associated with the metric in the 'Einstein frame' we confirm that the field equations derived from the non-Riemannian Einstein-Hilbert action coincide with the axi-dilat on sector of the tow-energy effective action derived from string theor y.