Mass gap in a Yang-Mills theory in the strong coupling limit

Abstract

We prove that in the limit of the coupling going to infinity a Yang-Mills theory is equivalent to a $λϕ^4$ theory with the dynamics ruled just by a homogeneous equation. This gives explicitly the Green function and the mass spectrum proving that such gauge theories are confining. The scalar glueball spectrum is then proven to be in fair agreement with lattice QCD computations but giving a different ground state coinciding with the $f_0(600)$ light unflavored meson.