Heat Kernel for Spin-3/2 Rarita-Schwinger Field in General Covariant Gauge

Abstract

The heat kernel for the spin-3/2 Rarita-Schwinger gauge field on an arbitrary Ricci flat space-time ($d>2$) is investigated in a family of covariant gauges with one gauge parameter $α$. The $α$-dependent term of the kernel is expressed by the spin-1/2 heat kernel. It is shown that the axial anomaly and the one-loop divegence of the action are $α$-independent, and that the conformal anomaly has an $α$-dependent total derivative term in $d=2m\geq6$ dimensions.