Wednesday, February 22, 2012

1202.4476 (Marco Bochicchio)

Yang-Mills mass gap at large-N, topological quantum field theory and

Marco Bochicchio
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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