The effective gravitational action of a massless chiral fermion and the absence of parity-odd contributions
Using the BPHZL renormalization scheme, the paper proves that the renormalized gravitational effective action for a massless chiral fermion up to fourth order in graviton fields contains no parity-odd contributions, is equivalent to half the action of a non-chiral Dirac fermion modulo parity-even counterterms, and yields a purely parity-even Weyl anomaly equal to half that of a Dirac fermion.