On tree-level higher order gravitational couplings in superstring theory

TL;DR

This paper analyzes tree-level graviton scattering amplitudes in superstring theory to identify constraints on higher order gravitational couplings, revealing the absence of certain terms and transcendentality patterns in the effective action.

Contribution

It provides the first detailed analysis of five- and six-graviton amplitudes at tree level up to order alpha'^8, uncovering new constraints on higher order couplings and transcendentality patterns.

Findings

Absence of R^5 terms in the effective action.

No zeta values of even weight up to order alpha'^8.

Constraints applicable to any superstring background and dimension.

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.