https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_existence_and_mass_gap Yang?Mills existence and mass gap (抜粋) Importance of Yang?Mills theory Most known and nontrivial (i.e. interacting) quantum field theories in 4 dimensions are effective field theories with a cutoff scale. Since the beta-function is positive for most models, it appears that most such models have a Landau pole as it is not at all clear whether or not they have nontrivial UV fixed points. This means that if such a QFT is well-defined at all scales, as it has to be to satisfy the axioms of axiomatic quantum field theory, it would have to be trivial (i.e. a free field theory).
Quantum Yang-Mills theory with a non-abelian gauge group and no quarks is an exception, because asymptotic freedom characterizes this theory, meaning that it has a trivial UV fixed point. Hence it is the simplest nontrivial constructive QFT in 4 dimensions. (QCD is a more complicated theory because it involves quarks.) (引用終り) 以上
