On tree-level higher order gravitational couplings in superstring theory

Abstract

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 like the absence of R^5 terms. Furthermore, some transcendentality constraints on the coefficients of the non-vanishing 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.

4 pages, RevTeX 4.1; v2: Results and discussion extended by the order alpha'^8. Again, no even zeta values occur at this order excluding curvature contact terms with MZV coefficients zeta(8), zeta(2) zeta(3)^2 and zeta(5,3), respectively; v3: streamlined and final version to appear in Physical Review Letters

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