Self – dual tensors and gravitational anomalies in 4 n + 2 dimensions

Starting from a manifestly Lorentz– and diffeomorphism–invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n + 2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two–dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two–dimensional complex Weyl–fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method. PACS: 11.30.Rd, 11.10.Kk, 11.30Cp;