Constructing gravity amplitudes from real soft and collinear factorization

Soft and collinear factorisations can be used to construct expressions for amplitudes in theoriesof gravity. We generalise the “half-soft” functions used previously to “soft-lifting” functions anduse these to generate tree and one-loop amplitudes. In particular we construct expressions forMHV tree amplitudes and the rational terms in one-loop amplitudes in the specific context ofN = 4 supergravity. To completely determine the rational terms collinear factorisation must alsobe used. The rational terms for N = 4 have a remarkable diagrammatic interpretation as arisingfrom algebraic link diagrams