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arXiv · 2412.02517

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

Matteo Giordano
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Abstract

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.

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Matteo Giordano. 2024-12-03. Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of $\mathrm{U}(1)_A$ symmetry. https://arxiv.org/abs/2412.02517

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