All Tree Amplitudes of 6D (2,0) Supergravity: Interacting Tensor Multiplets and the K3 Moduli Space

We present a twistorlike formula for the complete tree-level S matrix of six-dimensional (6D) (2,0) supergravity coupled to 21 Abelian tensor multiplets. This is the low-energy effective theory that corresponds to type IIB superstring theory compactified on a K3 surface. The formula is expressed as an integral over the moduli space of certain rational maps of the punctured Riemann sphere. By studying soft limits of the formula, we are able to explore the local moduli space of this theory, {[SO(5,21)]/[SO(5) x SO(21)]}. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D N = 4 Einstein-Maxwell theory.