COLOR-FLAVOR TRANSFORMATION AND ITS APPLICATIONS TO LATTICE FIELD THEORY

摘要

We overview the color-flavor transformation which has various applications to problems as diverse as lattice gauge theory, random network models, and dynamical systems with disorder. We present this transformation in the context of the fermionic sector of lattice QCD and induced lattice gluodynamics. Application to low energy QCD on a lattice leads to a theory where the inverse number of colors appears as expansion parameter. We use a saddle point approximation to estimate the partition function both in the pure mesonic sector and in the case of a single baryon on a mesonic background. The effective chiral Lagrangian of QCD is recovered up to the terms of order O(p~4). We also consider the color -flavor transformation applied to the pure lattice gluodynamics, in which the gauge theory is induced by a heavy chiral scalar field. The effective, color flavor transformed theory is expressed in terms of gauge singlet matrix fields carried by the lattice links.