Approaches to the gravitational spin-32 axial anomaly

The $\text{spin}\text{-}\text{3}\text{2}$ axial anomaly is discussed from various points of view. Two consistent theories for a $\text{spin}\text{-}\text{3}\text{2}$ field interacting with gravity are considered: supergravity and a real quantized $\text{spin}\text{-}\text{3}\text{2}$ field in a classical gravitational background. The Feynman graph method, the zeta function regularization method, the point splitting method and the topological method all yield the same result for the latter theory, in agreement with that first found by Christensen and Duff.