A gauge/gravity relation in the one-loop effective action

We identify an unusual new gauge/gravity relation: the one-loop effective action for a massive spinor in 2n-dimensional AdS space is expressed in terms of precisely the same function (a certain multiple gamma function) as the one-loop effective action for a massive charged scalar in 4n dimensions in a maximally symmetric background electromagnetic field (one for which the eigenvalues of F mu nu. are maximally degenerate, corresponding in four dimensions to a self-dual field, equivalently to a field of definite helicity), subject to the identification F-2 <-> Lambda, where Lambda is the gravitational curvature. Since these effective actions generate the low energy limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a nontrivial gauge/gravity relation at the non-perturbative level and at the amplitude level.