Constraining higher derivative supergravity with scattering amplitudes

We study supersymmetry constraints on higher derivative deformations of type IIB supergravity by consideration of superamplitudes. Combining constraints of on-shell supervertices and basic results from string perturbation theory, we give a simple argument for the nonrenormalization theorem of Green and Sethi, and some of its generalizations.

Figure 1

Factorization of the 6-point amplitude through one $D^n{R}^4$ vertex (shaded blob) and a pair of supergravity cubic vertices.

Figure 2

Factorization of the 6-point amplitude through a pair of $R^4$ vertices.