Supergravity divergences, supersymmetry and automorphic forms

Understand

We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the effective action.

• Our method makes use of tensorial differential equations that constrain these couplings.
• We study in detail the Fourier modes and wave-front sets of the associated automorphic functions and find that they are always associated to special nilpotent orbits.