In the comments on the post where Peter Woit kindly pointed to my blog (see here) there is some point about when a quantum field theory can be considered “trivial”. Indeed, this question is fairly well acquired for the expert of quantum field theory as there exists a theorem due to Michael Aizenman (see here) for the scalar field theory but this result only applies to theory with dimensions greater or equal 5. If the scalar theory is trivial for D=4 is an open and hotly debated question still far from being settled.
So, what should one mean by a “trivial” field theory? We can say that a quantum field theory becomes trivial when in some limit is a free theory. To become free a theory should have the coupling going to zero in the considered limit and only this that is meaningful. As it is largely known, for a gauge theory a propagator can depend on the choice of the gauge. But it is also true that for some theories the appearence of a free propagator and the corresponding behavior of higher n-point funtions is already a proof of triviality.
What does it happen to the running coupling of the Yang-Mills theory at lower momenta? A long time expectation has been that the running coupling of Yang-Mills theory should reach a non-trivial infrared fixed point, that is, it should have had a fixed value as the energy goes to zero. Lattice results said the opposite. But there is a glitch here. The problem is that we have not a clear understanding of what should be a proper definition of the running coupling in the infrared limit. People working on the lattice have chosen the definition taken from functional methods arosen with Alkofer and von Smekal. The computation on the lattice of this quantity shows that it goes to zero and no fixed point emerges. Different definitions have been proposed (see here for a review) but there are also experimental evidences, due to Giovanni Prosperi and his group and presented here, that the coupling at low momenta goes to zero.
All this gives a strong clue that Yang-Mills theory is a trivial theory in the infrared and shares a similar fate with the scalar theory.