Non-renormalization theorems in maximal supergravity

The control over nonabelian gauge invariances at the quantum level, which Andrei Alekseevich Slavnov brilliantly pioneered, plays a critical role in the study of the ultraviolet problem both in gauge theories and in theories of gravity. The recent dramatic cancellations of divergent contributions to certain BPS counterterm structures in maximal supergravity require a careful revisit of the applicable nonrenormalization theorems, based on local gauge invariances and on duality symmetries. In the end, these suffice to explain all the BPS counterterm cancellations found to date in maximal supergravity, both in four and in higher spacetime dimensions.