The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

Details The Effective Lagrangian of Three Dimensional Quantum Chromodynamics The Effective Lagrangian of Three Dimensional Quantum Chromodynamics

1992-04-23

arxiv.org/abs/hep-th/9204075v1

Int.J.Mod.Phys. A7 (1992) 7989-8000

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

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).

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