Chiral supergravity and anomalies

Similarily as in the Ashtekar approach, the translational Chern-Simons term is, as a generating function, instrumental for a chiral reformulation of simple (N=1) supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only decomposition of the gravitational fields into selfdual and antiselfdual modes, but also a splitting of the Rarita-Schwinger fields into their chiral parts in a natural way. In some detail, we also analyze the consequences for axial and chiral anomalies.