Axial Anomaly for Gravitino and Unconventional FP Ghosts

Abstract

The axial anomaly for the gravitino in a background gravitational field is obtained by using the new formalism of Hata and Kugo for supergravity with unconventional Faddeev-Popov (FP) ghosts. Despite the new FP ghosts have essentially different features from the ordinary ones it is shown that the anomaly leads to the same value as the ordinary one which is -21 times that of a spin 1/2 Majorana Fermion. This means that in the new formalism the part which contributes to the anomaly is the Lagrangian multiplier for gauge fixing and not FP ghosts in contrast to the case of the ordinary formalism. The relation between the canonical formalism of Hata-Kugo and the functional integral formalism is clarified. It is also shown that the axial anomaly is obtained within the framework of the path integral formalism by adopting the zeta-function regularization method.