Uniton Bundles

TL;DR

This paper adapts twistor methods to study unitons, revealing their equivalence to certain holomorphic bundles, confirming their rationality, and providing explicit examples in U(3).

Contribution

It introduces a twistor-based framework for analyzing unitons, establishing their correspondence with holomorphic bundles and confirming their rationality.

Findings

Unitons are equivalent to holomorphic bundles with additional structure.

Unitons are confirmed to be rational.

Constructed an explicit two-uniton example in U(3).

Abstract

We show that a twistor construction of Hitchin and Ward can be adapted to study unitons (harmonic spheres in a unitary group). Specifically, we show that unitons are equivalent to holomorphic bundles with extra structure over a rational ruled surface with energy given by Chern class. This equivalence allows us to confirm the conjecture of Wood that unitons are rational. We also construct an example of a two uniton in U(3) using this construction.