Zvi Bern gave a talk yesterday at the KITP in Santa Barbara entitled The S-Matrix Reloaded: Twistors, Unitarity, Gauge Theories and Gravity. He surveyed recent progress on computing perturbative amplitudes in QCD and N=4 supersymmetric Yang-Mills, some of which involves using twistor methods. The most striking thing though were his last few transparencies (here, here, and here). He notes that all previous studies of divergences in supergravity rely only on power-counting and supersymmetry, assuming that if these two principles allow a divergence to occur, it will. Actually doing the full computation to see if the divergences are there is too hard and no one has done it. Bern notes that in these arguments the extra structure seen by the recent twistor methods is not taken into account, and when one does this, so far all complete calculations show that N=8 supergravity has exactly the same degree of divergence as N=4 Yang-Mills, even though one would naively expect the supergravity amplitudes to have worse behavior. He ends by suggesting that “Serious re-examination of the UV properties of multi-loop N=8 supergravity using modern tools is needed.”
If N=8 supergravity turns out to be renormalizable, this raises an interesting question about string theory….