On Supergravity Amplitudes from Pure Spinor Strings

We use Pure Spinor String Theory to construct suitable building blocks to arrange the structure of supergravity amplitudes with n-points and at higher loops in a very convenient way. Following Mafra et al. proposal for N=4 super Yang-Mills amplitudes, we discuss its generalization to supergravity amplitudes. In particular, we first derive the building blocks for closed string amplitudes from closed vertices showing that, because of the factorization, several results of open string theory can be used; nevertheless, also new structures emerge. We provide a first list of these new ingredients and their BRST variations. Second, we analyze 4-point amplitudes showing how the different building blocks enter and finally we discuss the factorization of 5-point amplitudes in supergravity in terms of those structures.