Chiral supergravity and anomalies

Abstract

Similarly as in the Ashtekar approach, the translational Chern‐Simons term is, as a generating function, instrumental for a chiral reformulation of simple supergravity. After applying the algebraic Cartan relation between spin and torsion, the resulting canonical transformation induces not only a decomposition of the gravitational fields into selfdual and anti‐selfdual 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.