Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2012-02-20
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, latex
Scientific paper
In the large-N limit of pure SU(N) Yang-Mills, the ambient algebra of Wilson loops is known to be a type II_1 non-hyperfinite factor. Nevertheless, at the first 1/N non-trivial order, because of the mass gap and confinement, the connected two-point correlation function of local gauge invariant operators are conjectured to be an infinite sum of propagators of free massive fields. It is an open problem, most relevant to a complete solution of the glueball spectrum at large-N, whether or not the corresponding local algebra is hyperfinite. Yet, for the mass gap problem or for a partial solution of the glueball spectrum, one should consider hyperfinite subalgebras. We show that a hyperfinite sector is constructible by fluctuations around a trivial topological field theory underlying Yang-Mills at large N. The hyperfiniteness problem has been suggested by the author as one of several problems arising as a byproduct of the Simons Center workshop "Mathematical Foundations of Quantum Field Theory", Jan 16-20 (2012).
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