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$\chi$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$\chi$S results from a subtle balance between the density of Euclidean quark states and their mobility. SB$\chi$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.

arXiv comment4 pages, LaTeX, submitted to Physical Review Letters

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