Self-dual tensors and gravitational anomalies in 4n+2 dimensions
arXiv:hep-th/9808025 · doi:10.1016/S0550-3213(98)00626-9
Abstract
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.
20 pages, references added, misprints corrected
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