Instanton zero modes and β-functions in gauged supergravity

We prove that one loop infinities in N?3 gauged O(N) supergravities are produced only by zero modes both on de Sitter and gauge instanton backgrounds. This strongly suggests (in analogy with the super Yang-Mills case) that instantons may be used for establishing exact β-functions in supergravities. We also derive the general formula for the number of gauge instanton zero modes for arbitrary spin and find that the “magnetic moment” part of the contribution in the gauge β-function is completely due to zero modes.