The Color--Flavor Transformation of induced QCD

TL;DR

This paper applies Zirnbauer's 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-Nc limit.

Contribution

It extends the color-flavor transformation to a lattice gauge model with multiple generations of auxiliary fields and derives the resulting effective theory in arbitrary dimensions.

Findings

Effective action expressed in gauge singlet matrices on lattice links.

Analysis of saddle point equations in the large-Nc limit.

Investigation of dual lattices in 2D and 3D.

Abstract

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.