Two alternatives of spontaneous chiral symmetry breaking in QCD

TL;DR

This paper explores two different mechanisms for spontaneous chiral symmetry breaking in QCD, analyzing the role of eigenstates of the Dirac operator and drawing analogies with disordered systems.

Contribution

It introduces a novel analogy between chiral symmetry breaking in QCD and conductivity in disordered systems, proposing two distinct scenarios based on eigenstate properties.

Findings

SB$ ext{chi}$S can occur with zero condensate if low-density states have high mobility

SB$ ext{chi}$S can occur with non-zero condensate if mobility is suppressed

A formal analogy links pion decay constant to conductivity in disordered systems

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.