We study the violation of the uctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and oo equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of uctuation dis-sipation theorem in the oo-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for nite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in nite dimensional spin glasses.