Spherically Symmetric Istantons of the Scale Invariant SU(2) Gauged Grassmannian Model in d=4

TL;DR

This paper finds and classifies spherically symmetric instanton solutions in a scale-invariant SU(2) gauged Grassmannian model in four dimensions, introducing a new strong self-duality condition and solving it explicitly.

Contribution

It introduces a stronger self-duality condition for the model and explicitly constructs all spherically symmetric solutions satisfying this condition.

Findings

Explicit closed-form solutions for strong (anti)self-duality equations

Proof that these solutions are the only solutions of the strong self-duality equations

Derivation of the usual (anti)self-duality equations for axially symmetric fields

Abstract

(Anti)self-dual solutions of the scale invariant SU(2) gauged Grassmanian model are sought. A stronger (anti)selfduality condition for this system is defined, referred to as strong self-duality, and spherically symmetric solutions of this {\it strong} (anti)self-duality equations are found in closed form. It is verified that these are the only solutions of the strong (anti)self-duality equations. The usual (anti)self-duality equations for the axially symmetric fields are derived and seen to be not overdetermined.