  I derive constraints on the Dirac spectrum in the chirally symmetric phase of
a gauge theory with two massless fermion flavors. Using only general properties
of correlation functions of scalar and pseudoscalar bilinears, I prove that in
the chiral limit of vanishing quark mass $m$ all the corresponding
susceptibilities must be power series in $m^2$ with finite coefficients, from
which spectral constraints follow. I then use them to show that effective
breaking of the anomalous $\mathrm{U}(1)_A$ symmetry is allowed in the
$\mathrm{SU}(2)_A$ symmetric phase in the chiral limit, and leads to
distinctive spectral features: (i) the spectral density must develop a singular
$m^4/\lambda$ peak as $m\to 0$, (ii) the two-point eigenvalue correlator of
near-zero modes must be singular, and (iii) near-zero modes cannot be
localized. Moreover, in the symmetric phase the topological charge distribution
must be indistinguishable from that of an ideal gas of instantons and
anti-instantons of vanishing density, to leading order in the fermion mass.
