Vanishing one-loop function in gauged N>4 supergravity

In O(N) extended supergravity theories, the usual arguments for one-loop finiteness (modulo topological terms) cease to apply when the internal symmetry is gauged because of the appearance of a cosmological constant related to the gauge coupling e. For N<~4, we find that infinite renormalizations are required. Remarkably, the particle content of theories with N>4 results in a cancellation of these infinities, implying, in particular a vanishing one-loop (e) function.