On tree-level higher order gravitational couplings in superstring theory

TL;DR

The scattering amplitudes of five and six gravitons at tree level in superstring theory are considered and their power series expansions in the Regge slope α' are analyzed through the order α'(8) showing some interesting constraints on higher order gravitational couplings in the effective superstring action such as the absence of R(5) terms.

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.

Figures (1)

• Figure 1: Diagrams contributing at the order $\alpha'^{3+m}$ to the five--graviton amplitude.