Large N phase transitions under scaling and their uses

Details Large N phase transitions under scaling and their uses Large N phase transitions under scaling and their uses

2009-06-29

arxiv.org/abs/0906.5299v1

Physics

High Energy Physics

High Energy Physics - Theory

29p -- Lecture notes at Zakopane, 5.31-6.10, 2009

Scientific paper

The eigenvalues of Wilson loop matrices in SU(N) gauge theories in dimensions 2,3,4 at infinite N are supported on a small arc on the unit circle centered at $z=1$ for small loops, but expand to the entire unit circle for large loops. These two regimes are separated by a large N phase transition whose universal properties are the same in d=2,3 and 4. Hopefully, this large N universality could be exploited to bridge traditional perturbation theory calculations, valid for small loops, with effective string calculations for large loops. A concrete case of such a calculation would obtain analytically an estimate of the large N string tension in terms of the perturbative scale Lambda(QCD,N).

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