Pure spinor indications of ultraviolet finiteness in D=4 maximal supergravity
The ultraviolet divergences of amplitude diagrams in maximal supergravity
are characterised by a first possible divergence at seven loops for the 4-point
amplitude (logarithmic) and, in its absence, at eight loops. We revisit the
pure spinor superfield theory results of [arXiv:1412.5983], stating the absence
of the divergence originating in the 4-point 7-loop amplitude as well
as those of more than seven loops. The analysis, performed in terms of the
one-particle irreducible loop structures giving rise to the divergences, is extended, especially with respect to the limits on the dimension for finiteness.
The results correspond to those mentioned, known from other approaches, indicating an ultraviolet finiteness of maximal supergravity in D = 4.