The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

TL;DR

This paper derives the low energy effective Lagrangian for three-dimensional QCD with an even number of flavors, revealing spontaneous flavor symmetry breaking and connecting it to models of quantum anti-ferromagnetism.

Contribution

It introduces a nonlinear sigma model on the Grassmannian and incorporates Chern--Simons terms, providing a novel effective description of 3D QCD.

Findings

Parity is not spontaneously broken.

Global flavor symmetry is spontaneously broken.

Effective Lagrangian describes long wavelength excitations in quantum anti-ferromagnets.

Abstract

We consider the low energy limit of three dimensional Quantum Chromodynamics with an even number of flavors. We show that Parity is not spontaneously broken, but the global (flavor) symmetry is spontaneously broken. The low energy effective lagrangian is a nonlinear sigma model on the Grassmannian. Some Chern--Simons terms are necessary in the lagrangian to realize the discrete symmetries correctly. We consider also another parametrization of the low energy sector which leads to a three dimensional analogue of the Wess--Zumino--Witten--Novikov model. Since three dimensional QCD is believed to be a model for quantum anti--ferromagnetism, our effective lagrangian can describe their long wavelength excitations (spin waves).