On the complete analytic structure of the massive gravitino propagator in four-dimensional de Sitter space

TL;DR

This paper provides a complete analytic representation of the massive gravitino propagator in four-dimensional de Sitter space using Heun functions, revealing detailed structure and behavior of the propagator's components.

Contribution

The authors express all weight functions in the gravitino propagator through Heun functions, completing previous partial results with explicit formulas and analysis.

Findings

Weight functions are expressed via Heun functions.

Two distinct ranges of the independent variable are identified.

Plots and series truncations illustrate the behavior of the propagator.

Abstract

With the help of the general theory of the Heun equation, this paper completes previous work by the authors and other groups on the explicit representation of the massive gravitino propagator in four-dimensional de Sitter space. As a result of our original contribution, all weight functions which multiply the geometric invariants in the gravitino propagator are expressed through Heun functions, and the resulting plots are displayed and discussed after resorting to a suitable truncation in the series expansion of the Heun function. It turns out that there exist two ranges of values of the independent variable in which the weight functions can be divided into dominating and sub-dominating family.