Constraints on Tree-Level Higher Order Gravitational Couplings in Superstring Theory

We consider the scattering amplitudes of five and six gravitons at tree level in superstring theory. Their power series expansions in the Regge slope alpha' are analyzed through the order alpha'(8) showing some interesting constraints on higher order gravitational couplings in the effective superstring action such as the absence of R-5 terms. Furthermore, some transcendentality constraints on the coefficients of the nonvanishing couplings are observed: the absence of zeta values of even weight through the order alpha'(8) like the absence of zeta(2)zeta(3)R-6 terms. Our analysis is valid for any superstring background in any space-time dimension, which allows for a conformal field theory description.