Constraints on the Dirac spectrum from chiral symmetry restoration
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915034771226624 |
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| author | Giordano, Matteo |
| author_facet | Giordano, Matteo |
| contents | 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 fermion mass $m$ the corresponding susceptibilities and all their derivatives with respect to $m^2$ must be finite. I then use the resulting spectral constraints 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 $O(m^4)/λ$ 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 $m$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constraints on the Dirac spectrum from chiral symmetry restoration Giordano, Matteo High Energy Physics - Lattice Disordered Systems and Neural Networks High Energy Physics - Phenomenology High Energy Physics - Theory 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 fermion mass $m$ the corresponding susceptibilities and all their derivatives with respect to $m^2$ must be finite. I then use the resulting spectral constraints 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 $O(m^4)/λ$ 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 $m$. |
| title | Constraints on the Dirac spectrum from chiral symmetry restoration |
| topic | High Energy Physics - Lattice Disordered Systems and Neural Networks High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.03546 |