Momentum cut-off regularisation leads to non-covariant results, i.e., it breaks the Poincaré covariance of the theory. Is there any guarantee that Poincaré covariance is always restored when we remove the cut-off? Or can this symmetry be anomalous? Is there any topological argument about the Poincaré group that would automatically rule out any anomaly?
Assume that the regulator is the only source of non-covariance (for example, if there are gauge fields, the fixing condition is covariant as opposed to, say, Coulomb). Also, assume that Poincaré is a global symmetry of the classical theory (i.e., no gravity).