I discuss chiral symmetry restoration in the chiral limit $m\to 0$ of QCD with two light quark flavours of mass $m$, focussing on its consequences for scalar and pseudoscalar susceptibilities, and on the resulting constraints on the Dirac spectrum. I show that $\mathrm{ U}(1)_A$ symmetry remains broken in the $\mathrm{ SU}(2)_A$ symmetric phase if the spectral density $\rho(\lambda;m)$ develops a singular near-zero peak, tending to $O(m^4)/\lambda$ in the chiral limit. Moreover, $\mathrm{ SU}(2)_A$ restoration requires that the number of modes in the peak be proportional to the topological susceptibility, indicating that such a peak must be of topological origin.
Categories: hep-lat cond-mat.dis-nn hep-ph hep-th