Chiral Symmetry Breaking in 2+1 dimensions due to Sphalerons
Indranil Dasgupta, L. C. R. Wijewardhana
Abstract
In 2+1 dimensional gauge thories with SU(Nc) color and 2Nf flavors of quarks in the fundamental representation, sphalerons, if present may lead to quark condensation and chiral symmetry breaking. The effect is similar to instanton induced chiral symmetry breaking in 3+1 dimensions and is due to the interaction of quark propagators with sphalerons. The existence of sphalerons requires that color symmetries be broken by a Higgs in the fundamental representation. We show that the sphaleron effect may persist for arbitrarily large Nf but vanishes along with the mass of the gauge fields corresponding to broken generators of SU(Nc). The effect is inherently non-Abelian and absent for QED.
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