# Topological Phases and Confinement

I recently attended a talk in which the speaker defined a topological phase as "A phase which has a gap above the ground state for bulk excitations in the thermodynamic limit." I am interested in what sense then can we think of confinement in non-Abelian Yang-Mills theories as topological phases.

What I'm looking for are the analogies; what would the thermodynamic limit and the bulk excitations mean if we were talking about a YM theory (QCD, for instance). The thermodynamic limit is the number of particles $N\to\infty$, which I suppose we can think of as the number of Feynman diagrams (order of the loops) growing as large as possible. "The bulk" seems a bit more vague (which is perhaps because of my definition), but it seems like bound states of quarks is the appropriate notion for that.

So, is it possible to (correctly) say something like "QCD is a topological phase for the standard model"? If not, is there a clear reason why this is not the case?

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You can see Aharony et al's paper on Hagedorn deconfinement transition. (in general see Kyriakos's PhD papers) They consider the large N_c limit of free Yang-Mill's theory on compact space-time. That theory seems to be permanently confined. –  user6818 May 28 '13 at 19:34