Higgs-free confinement hierarchy in five colour QCD

Introduction It is already known,1)–3) that SU(N) QCD can lower the energy of its vacuum with a monopole background field along the Abelian directions, where the Abelian components are equal in magnitude but orthogonal in real space.2), 3) This orthogonality, while of no special consequence in SU(3) QCD in three space dimensions, does have consequences when the number of Abelian directions is greater than three. As noted originally by Flyvberg,2) SU(N ≥ 5) QCD cannot realise its true minimum because four orthogonal vectors cannot fit in three dimensions. I shall call a system kept from reaching its true lowest energy state by a lack of spatial dimensions dimensionally frustrated. The effective ground state energy of the monopole condensate is a non-analytic expression in the Cartan components H(i). However, its form strongly suggests that the lowest physically available energy state is the one that leaves the effective condensate felt by each of the off-diagonal (valence) gluons equal in magnitude, or as close to it as can be realised. This is the motivation for my condensate ansatz. The lowest energy state allowed by it leaves the (matter-antimatter pair of) gluons associated with one root vector very strongly confined, another very weakly confined, and the rest confined with identical intermediate strength. Examining the dynamics at intermediate energy scales where the strongly confined dynamics have dropped out finds an emergent three-colour QCD accompanied by gluons whose dynamics no longer conform to a special unitary symmetry group. They do however form two sixdimensional representations of SU(3). One of these representations consists of the weakly confined valence gluons. Exactly one unconfined massless Abelian gauge field (photon) can be found by taking linear combinations of the accompanying Abelian gluons.