The Color--Flavor Transformation of induced QCD

Details The Color--Flavor Transformation of induced QCD The Color--Flavor Transformation of induced QCD

2005-06-30

arxiv.org/abs/hep-lat/0506035v1

Int.J.Mod.Phys. A20 (2005) 4965-4994

Physics

High Energy Physics

High Energy Physics - Lattice

24 pages, 6 figures, to appear in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X05025401

The Zirnbauer's color-flavor transformation is applied to the $U(N_c)$ lattice gauge model, in which the gauge theory is induced by a heavy chiral scalar field sitting on lattice sites. The flavor degrees of freedom can encompass several `generations' of the auxiliary field, and for each generation, remaining indices are associated with the elementary plaquettes touching the lattice site. The effective, color-flavor transformed theory is expressed in terms of gauge singlet matrix fields carried by lattice links. The effective action is analyzed for a hypercubic lattice in arbitrary dimension. We investigate the corresponding d=2 and d=3 dual lattices. The saddle points equations of the model in the large-$N_c$ limit are discussed.

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