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

## TL;DR

This paper derives a twistor-like formula for the complete tree-level S matrix of 6D $(2,0)$ supergravity with tensor multiplets, connecting it to string compactification on K3 and reducing to 4D Einstein-Maxwell theory.

## Contribution

It provides the first explicit twistor-like integral formula for 6D $(2,0)$ supergravity coupled to tensor multiplets, and explores its moduli space and dimensional reduction.

## Key findings

- Derived a twistor-like formula for 6D supergravity amplitudes.
- Explored the moduli space of the theory via soft limits.
- Obtained a new formula for 4D $
abla$=4 Einstein-Maxwell amplitudes.

## Abstract

We present a twistor-like formula for the complete tree-level S matrix of 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 $\mathrm{K}3$ 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, ${SO(5,21)\over SO(5)\times SO(21)}$. Finally, by dimensional reduction, we also obtain a new formula for the tree-level S matrix of 4D $\mathcal{N}=4$ Einstein-Maxwell theory.