Chiral Symmetry Breaking in 2+1 dimensions due to Sphalerons

Abstract

In 2+1 dimensional gauge thories with $SU(N_c)$ color and $2N_f$ 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 $N_f$ but vanishes along with the mass of the gauge fields corresponding to broken generators of $SU(N_c)$. The effect is inherently non-Abelian and absent for QED.

15 pages, LaTex, 1 figure, uses epsf

References in corpus (3)

• Instantons and the Chiral Phase Transition
• Fermion zero-modes of a new constrained instanton in Yang-Mills-Higgs theory
• The imaginary time Path Integral and non-time-reversal-invariant- saddle points of the Euclidean Action