Absence of Goldstone boson for a U( N) gauge theory with Dirac-Kähler fermions on the lattice

Abstract

We use the gauge-invariant Dirac-Kähler lattice action, directly in terms of quark fields, in order to study the chiral symmetry breaking of the quarks at strong coupling for a U( N) gauge theory. We find that, in contrast with the case of Kogut-Susskind fermions, the dynamical quark mass does not break any continuous chiral symmetry of the lattice action and, hence, no pion-like exact Goldstone particle is present on the lattice.