Arguments Against a Finite N=8 Supergravity

Understand

I present arguments based on dispersion theory and the existence of charged BPS states of small charge, that maximally supersymmetric SUGRA is not a finite theory.

• The essence of the argument is that the perturbative construction of the theory implies that scattering amplitudes are invariant under a continuous SU(8) global symmetry, which is broken by contributions from virtual BPS states.
• Conventional estimates of the contributions of those states above production threshold, shows that they should be order one.
• If the amplitude satisfies a dispersion relation with a finite number of subtractions, as has recently been argued by Giddings and Porto [1], then SU(8) violating amplitudes appear at finite orders in the low energy expansion.