Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of $\mathrm{U}(1)_A$ symmetry
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915047002865664 |
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| author | Giordano, Matteo |
| author_facet | Giordano, Matteo |
| contents | 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 $ρ(λ;m)$ develops a singular near-zero peak, tending to $O(m^4)/λ$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_02517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of $\mathrm{U}(1)_A$ symmetry Giordano, Matteo High Energy Physics - Lattice Disordered Systems and Neural Networks High Energy Physics - Phenomenology High Energy Physics - Theory 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 $ρ(λ;m)$ develops a singular near-zero peak, tending to $O(m^4)/λ$ 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. |
| title | Constraints on the Dirac spectrum from chiral symmetry restoration and the fate of $\mathrm{U}(1)_A$ symmetry |
| topic | High Energy Physics - Lattice Disordered Systems and Neural Networks High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.02517 |