The weak-coupling Yang–Mills mass gap conjecture

Let $H^g$ be the Hamiltonian reconstructed from the four-dimensional Yang–Mills theory, let $g_0\in[0,1[$, and let $\operatorname{spec}(H^g)$ denote its spectrum. A mass gap is a positive lower bound separating the vacuum eigenvalue $0$ from the rest of the spectrum.

Weak-coupling Yang–Mills mass gap conjecture. For any bare coupling constant $g\in[0,g_0[$, the spectrum of $H^g$ contains $0$ as a simple eigenvalue for the vacuum eigenstate and satisfies

$$\operatorname{spec}(H^g)\subset\{0\}\cup[\eta^g,+\infty[,$$

for an $\eta^g>0$, with $\eta^g=O(g^{2(n+1)})$ for every $n\in\mathbf{N}_0$. In particular, there is a mass gap only if $g>0$, and the group $G$ must be non-abelian.

This is the paper's explicit weak-coupling spectral formulation of the mass-gap claim. The supplied text does not state that it has been proved or refuted.