QCD in 2+1 dimensions with N species of fermions, analyzed in the 1/N expansion, is shown to exhibit a chiral and confinement phase transition as N approaches a critical value Nc. For N>Nc, the theory is chirally symmetric and deconfined. For NNc, chiral symmetry is broken and confinement sets in at momentum scales less than the fermion mass. The reliability of the 1/N expansion when N{}Nc is discussed, and the behavior of this theory is contrasted with QCD in 3+1 dimensions.
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Thomas Appelquist (1990) studied this question.
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