Higher spin Killing spinors on 3-dimensional manifolds

TL;DR

This paper introduces higher spin Killing spinors on 3D Riemannian manifolds, providing explicit examples on the sphere and hyperbolic space, and establishing a rigidity result for such manifolds.

Contribution

It defines higher spin Killing spinors in arbitrary dimensions, proves a rigidity theorem in 3D, and derives explicit solutions on key geometries.

Findings

Rigidity result for 3D manifolds with higher spin Killing spinors

Explicit expressions for these spinors on the 3-sphere and hyperbolic space

Analysis of the Killing spinor equation on integral spin bundles

Abstract

We define higher spin Killing spinors on Riemannian spin manifolds in arbitrary dimension and study them in detail in dimension three. We prove a rigidity result for 3-dimensional manifolds admitting higher spin Killing spinors and give expressions for higher spin Killing spinors on the 3-sphere and the 3-hyperbolic space explicitly. We also investigate the Killing spinor type equation on integral spin bundles.