On Higher Derivative Couplings in Theories with Sixteen Supersymmetries

We give simple arguments for new non-renormalization theorems on higher derivative couplings of gauge theories to supergravity, with sixteen supersymmetries, by considerations of brane-bulk superamplitudes. This leads to some exact results on the effective coupling of D3-branes in type IIB string theory. We also derive exact results on higher dimensional operators in the torus compactification of the six dimensional (0, 2) superconformal theory.