Chiral-symmetry breaking in continuum two-dimensional QCD by an infrared method

Estimates of 〈ψ¯ψ〉 in the quenched approximation for two-dimensional QCD (${\mathrm{QCD}}_2$) are obtained, based upon a continuum, infrared approximation previously developed for ${\mathrm{QED}}_2$. Nontrivial gauge-invariant extensions are devised for general SU(N), and computations are carried out for finite N(=2,3) and in the large-N limit. Specifically non-Abelian structure appears for finite N, while the large-N limit displays an ‘‘effective Abelian’’ simplification. A nonzero value of 〈ψ¯ψ〉 is found in the chiral limit for all N; in the limit N→∞, 〈ψ¯ψ〉∼-${\mathrm{gN}}^{3/2}$, independently of the value g. (This generalized a previous result of Zhitnitsky, who found a similar combination in the planar limit, with ${\mathrm{gN}}^{1/2}$ fixed.)