The structure of the Yang-Mills spectrum for arbitrary simple gauge algebras

The mass spectrum of pure Yang-Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common to all algebras, while the lightest $C=-$ three-quasigluon glueballs only exist when the gauge algebra is A${}_{r\ge 2}$, that is in particular $\mathfrak{s}\mathfrak{u}(N\ge 3)$. Higher-lying $C=-$ glueballs are shown to exist only for the A${}_{r\ge 2}$, D${}_{\mathrm{o}\mathrm{d}\mathrm{d}-r\ge 4}$ and E${}_6$ gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result, the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an $\mathfrak{s}\mathfrak{u}(N)$ gauge algebra within 't Hooft’s large-$N$ limit.