Ultraviolet Sensitivity in Higher Dimensions

We calculate the first three Gilkey-DeWitt (heat-kernel) coefficients, a0, a1 and a2, for massive particles having the spins of most physical interest in n dimensions, including the contributions of the ghosts and the fields associated with the appropriate generalized Higgs mechanism. By assembling these into supermultiplets we compute the same coefficients for general supergravity theories, and show that they vanish for many examples. One of the steps of the calculation involves computing these coefficients for massless particles, and our expressions in this case agree with -- and extend to more general background spacetimes -- earlier calculations, where these exist. Our results give that part of the low-energy effective action which depends most sensitively on the mass of heavy fields once these are integrated out. These results are used in hep-th/0504004 to compute the sensitivity to large masses of the Casimir energy in Ricci-flat 4D compactifications of 6D supergravity.