Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD
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| Format: | Preprint |
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2023
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| _version_ | 1866914805835628544 |
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| author | Kovacs, Tamas G. |
| author_facet | Kovacs, Tamas G. |
| contents | We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_04208 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD Kovacs, Tamas G. High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures. |
| title | Fate of Chiral Symmetries in the Quark-Gluon Plasma from an Instanton-Based Random Matrix Model of QCD |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2311.04208 |