Up to order four in graviton fields the effective action for a massless chiral fermion is parity-even and equals half the corresponding action for a non-chiral Dirac fermion, with the Weyl anomaly likewise parity-even and halved.
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The effective gravitational action of a massless chiral fermion and the absence of parity-odd contributions
Up to order four in graviton fields the effective action for a massless chiral fermion is parity-even and equals half the corresponding action for a non-chiral Dirac fermion, with the Weyl anomaly likewise parity-even and halved.