Abstract
We examine the tree level four-point scattering amplitude for gravitons and dilatons in the heterotic string theory. The leading order effective lagrangian which reproduces this amplitude is quartic in a generalized curvature containing the dilaton contributions. This curvature is derived from a suitably generalized symmetric connection, and is such, that, after performing a Weyl rescaling on the metric, all ϱφ terms are removed from the effective action. We derive the equations of motion for the dilaton and rescaled metric and discuss a possible compactification solution.
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