Periodic instantons and the loop group

TL;DR

This paper constructs a broad class of periodic instantons and provides evidence that all such instantons can be generated, linking them to loop group orbits and confirming a conjecture in the field.

Contribution

It introduces a comprehensive construction of periodic instantons and supports the conjecture connecting them to loop group orbits on extended Lie algebras.

Findings

Constructed a large class of periodic instantons.

Supported the conjecture relating instantons to loop group orbits.

Confirmed the conjecture of Garland and Murray.

Abstract

We construct a large class of periodic instantons. Conjecturally we produce all periodic instantons. This confirms a conjecture of Garland and Murray that relates periodic instantons to orbits of the loop group acting on an extension of its Lie algebra.