The Color--Flavor Transformation of induced QCD

TL;DR

This paper applies the color-flavor transformation to an induced lattice gauge model with heavy scalar fields, deriving an effective theory in terms of gauge singlet matrices and analyzing saddle points in the large-N limit.

Contribution

It introduces a novel application of the color-flavor transformation to induced QCD models with multiple generations of auxiliary fields on a lattice.

Findings

Effective gauge singlet matrix fields are derived for the transformed theory.

Saddle point equations are formulated and analyzed in the large-N limit.

The approach is applicable to hypercubic lattices in arbitrary dimensions.

Abstract

The color-flavor transformation is applied to the U(N) 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. The saddle points equations of the model in the large-N limit are discussed.