An exact unstable mode of self-similar Yang–Mills solutionsin 5+1 dimensions

Self-similar solutions play an important role in the formation of singularities in the Yang–Mills equations. In five space dimensions, these equations admit infinitely many self-similar solutions with an increasing number of unstable modes. It was observed numerically that all excited profiles share the least unstable eigenvalue $λ=5$. We explain this remarkable spectral property by an elementary construction of the corresponding eigenfunction in terms of the profile.