ON THE ISOMORPHIC DESCRIPTION OF CHIRAL SYMMETRY BREAKING BY NONUNITARY LIE GROUPS

Abstract

It is well known that chiral symmetry breaking (χSB) in QCD with Nf = 2 light quark flavors can be described by orthogonal groups as O (4) → O (3), due to local isomorphisms. Here we discuss the question how specific this property is. We consider generalized forms of χSB involving an arbitrary number of light flavors of continuum or lattice fermions, in various representations. We search systematically for isomorphic descriptions by nonunitary, compact Lie groups. It turns out that there are a few alternative options in terms of orthogonal groups, while we did not find any description entirely based on symplectic or exceptional Lie groups. If we adapt such an alternative as the symmetry breaking pattern for a generalized Higgs mechanism, we may consider a Higgs particle composed of bound fermions and trace back the mass generation to χSB. In fact, some of the patterns that we encounter appear in technicolor models. In particular if one observes a Higgs mechanism that can be expressed in terms of orthogonal groups, we specify in which cases it could also represent some kind of χSB of techniquarks.