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

TL;DR

This paper derives the heat kernel for the spin-3/2 Rarita-Schwinger field in Ricci-flat spacetimes across covariant gauges, revealing gauge independence of anomalies and gauge-dependent total derivative terms in higher dimensions.

Contribution

It provides an explicit expression for the heat kernel of the Rarita-Schwinger field in arbitrary covariant gauges on Ricci-flat backgrounds, including gauge dependence analysis.

Findings

Axial anomaly and one-loop divergence are gauge-independent.

Conformal anomaly includes gauge-dependent total derivative terms in higher dimensions.

The $eta$-dependent term relates to the spin-1/2 heat kernel.

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 $\alpha$. The $\alpha$-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 $\alpha$-independent, and that the conformal anomaly has an $\alpha$-dependent total derivative term in $d=2m\geq6$ dimensions.