A set of Lorentz invariant differential operators can be used to transmute tree-level amplitudes into new ones. This technique allows one to generate the Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon and nonlinear sigma model amplitudes (among others) directly from a particular gravitational amplitude (of a graviton coupled to a dilaton and a two-form). Explicitly, the transmutation operations correspond to changing the spin of a particle and then reorganizing the colour structure appropriately.

The transmutation described here allows one to move seamlessly between the S matrix elements of superficially very different theories. Particularly exciting is the 'unified web of theories' depicted in Figure 1, which shows how interacting theories of various spins and symmetry groups are interconnected by these operations. The Adler zero in the soft limit of scalar field theories can now be interpreted as the transmutation of a soft theorem from a spinning theory. This suggests, in light of recent work on sub-leading soft theorems, that the soft behaviour of certain scalar theories is like-wise tightly constrained by asymptotic symmetries.