Massive Gravitino Propagator in Maximally Symmetric Spaces and Fermions in dS/CFT

TL;DR

This paper derives the massive spin 3/2 propagator in maximally symmetric spaces using Heun's functions and explores the implications for fermions in the dS/CFT correspondence, revealing complex conformal dimensions.

Contribution

It extends propagator calculations to massive spin 3/2 fields in various dimensions using Heun's functions and analyzes the dual operator dimensions in dS/CFT.

Findings

Propagator expressed in terms of Heun's functions for arbitrary dimensions and masses.

Dual operator conformal dimension is always complex across all dimensions and masses.

Implications for fermions in dS/CFT are discussed.

Abstract

We extend the method of calculation of propagators in maximally symmetric spaces (Minkowski, dS, AdS and their Euclidean versions) in terms of intrinsic geometric objects to the case of massive spin 3/2 field. We obtain the propagator for arbitrary space-time dimension and mass in terms of Heun's function, which is a generalization of the hypergeometric function appearing in the case of other spins. As an application of this result we calculate the conformal dimension of the dual operator in the recently proposed dS/CFT correspondence both for spin 3/2 and for spin 1/2. We find that, in agreement with the expectation from analytic continuation from AdS, the conformal dimension of the dual operator is {\it always} complex (i.e. it is complex for every space-time dimension and value of the mass parameter). We comment on the implications of this result for fermions in dS/CFT.