The Double Copy from Graph Theory

The double copy is a powerful tool connecting gauge theoretic and gravitational scattering amplitudes. It was originally derived from string theory, relating the tree level amplitudes of closed string amplitudes to two copies of open string amplitudes. In the field theory limit, this reduces to being able to obtain tree-level graviton amplitudes from the "square" of tree-level gluon amplitudes. At the same time, these field theory amplitudes have surprisingly simple expressions in certain (MHV) helicity sectors, known as the Hodges' formula (gravity), and the Parke-Taylor formula (gauge theory). In this talk I will review the double copy connection between these two formulae, employing basic concepts in graph theory, and tease the generalisation to arbitrary helicity configurations using twistor space.