On the Moduli Space of Yang–Mills Fields on $$ \mathbb{R}^4 $$

Abstract

We consider the problem of description of the structure of the moduli space of Yang–Mills fields on \( \mathbb{R}^4 \) with gauge group G. According to harmonic spheres conjecture, this moduli space should be closely related to the space of harmonic spheres in the loop space ΩG. Since the structure of the latter space is much better understood, the proof of conjecture will help to clarify the structure of the moduli space of Yang–Mills fields. We propose an idea how to prove the harmonic spheres conjecture using the twistor methods.