Delocalised Spinors

TL;DR

This paper analyzes solutions to the Weyl equation in instanton backgrounds, revealing their asymptotic behavior and how they encode geometric and symmetry information of the instantons.

Contribution

It demonstrates that delocalized Weyl solutions asymptotically resemble localized spinors, capturing key geometric features of the instanton background.

Findings

Solutions are normalisable and regular in four-space.

Asymptotics are given by linear combinations of singular free solutions.

Asymptotic data captures geometry and symmetry of instantons.

Abstract

Solutions to the four-dimensional Euclidean Weyl equation in the background of a general JNR N-instanton are known to be normalisable and regular throughout four-space. We show that these solutions are asymptotically given by a linear combination of simple singular solutions to the free Weyl equation, which can be interpreted as localised spinors. The `spinorial' data parameterising the asymptotics of the delocalised solutions to the Weyl equation in the presence of the instanton almost determines the background instanton, yet not completely. However, it captures the geometry and symmetry of the underlying instanton configuration.