Two alternatives of spontaneous chiral symmetry breaking in QCD

Abstract

Considering QCD in an Euclidean box, the mechanism of spontaneous breaking of chiral symmetry (SB$χ$S) is analyzed in terms of average properties of lowest eigenstates of the Dirac operator. A formal analogy between the pion decay constant and conductivity in disordered systems is established. It follows that SB$χ$S results from a subtle balance between the density of Euclidean quark states and their mobility. SB$χ$S can be realized either with $<\bar q q > =0$, provided the low density of states is compensated by a high mobility, or with a non-vanishing condensate, provided the mobility is suppressed. It is conjectured that the first case corresponds to extended whereas the latter case to (weakly) localized quark states.