标题： 从手征对称性恢复对狄拉克谱的约束以及$\mathrm{U}(1)_A$对称性的命运 显示英文标题

标题： Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of $\mathrm{U}(1)_A$ symmetry

摘要： 我讨论在QCD的手征极限$m\to 0$下具有两个轻夸克味质量$m$的情况下的手征对称性恢复，重点探讨其对标量和伪标量灵敏度的影响，以及对狄拉克谱的约束。 我表明，如果谱密度$\rho(\lambda;m)$在接近零处出现奇异峰，趋向于$O(m^4)/\lambda$在手征极限中，$\mathrm{U}(1)_A$对称性在$\mathrm{SU}(2)_A$对称相中仍然被破坏。 此外，$\mathrm{SU}(2)_A$恢复要求峰中的模式数量与拓扑灵敏度成比例，这表明这样的峰必须起源于拓扑。 显示英文摘要

摘要： 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.