  I discuss the possible effects of a finite density of localised near-zero
Dirac modes in the chiral limit of gauge theories with $N_f$ degenerate
fermions. I focus in particular on the fate of the massless quasi-particle
excitations predicted by the finite-temperature version of Goldstone's theorem,
for which I provide an alternative and generalised proof based on a Euclidean
${\rm SU}(N_f)_A$ Ward-Takahashi identity. I show that localised near-zero
modes can lead to a divergent pseudoscalar-pseudoscalar correlator that
modifies this identity in the chiral limit. As a consequence, massless
quasi-particle excitations can disappear from the spectrum of the theory in
spite of a non-zero chiral condensate. Three different scenarios are possible,
depending on the detailed behaviour in the chiral limit of the ratio of the
mobility edge and the fermion mass, which I prove to be a renormalisation-group
invariant quantity.
