A Center-symmetric 1/N expansion
Oct, 2004Citations per year
Abstract:
The free energy of U(N) gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for SU(N) lattice gauge theory and show that it uniquely describes center-symmetric minimal action orbits in the limit of infinite lattice volume. The leading contribution to the free energy in the 1/N expansion about this background is of O(N^0) rather than O(N^2) as one finds when the center symmetry is spontaneously broken. The contribution of planar 't Hooft diagrams to the free energy is O(1/N^2) and sub-leading in this case. The change in behavior of the diagrammatic expansion is traced to Linde's observation that the usual perturbation series of non-Abelian gauge theories suffers from severe infrared divergences. This infrared problem does not arise in a center-symmetric expansion. The 't Hooft coupling \lambda=g^2 N is found to decrease proportional to 1/\ln(N) for large N. There is evidence of a vector-ghost in the planar truncation of the model.- 11.15.Pg
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- gauge field theory: U(N)
- background field
- expansion 1/N
- Wilson loop
- finite temperature
- perturbation theory: higher-order
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