Pseudoparticles and massless fermions in two dimensions

The role of pseudoparticles in the breakdown of chiral U(N) symmetry is studied in a two-dimensional model. Chiral U(1) is always destroyed by the axial-vector anomaly. For N = 2 chiral SU(N) is also spontaneously broken yielding massive fermions and three (decoupled) Goldstone bosons. For N 3 the fermions remain massless. Realistic four-dimensional theories are believed to behave in a similar way but the critical N above which the fermions cease to be massive is not known in four dimensions.