On the trace anomaly of a Weyl fermion

Recent studies have suggested that the trace anomaly of chiral fermions
in four dimensions coupled to gravity might contain an imaginary part
proportional to the Pontryagin density.
To test the claim we describe a calculation of the trace anomaly
of a Weyl fermion by employing Fujikawa's method supplemented by a scheme,
based on the Pauli-Villars regularisation, that allows to fix a consistent
regulator. We find that the trace anomaly of a Weyl fermion is given by half
the trace anomaly of a Dirac fermion, and no imaginary part proportional to
the Pontryagin density is seen to arise.