Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929439369068544 |
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| author | Fejos, G. Hatsuda, T. |
| author_facet | Fejos, G. Hatsuda, T. |
| contents | Renormalization group flows of the $SU(N_f)\times SU(N_f)$ symmetric Ginzburg-Landau potential are calculated for a general number of flavors, $N_f$. Our approach does not rely on the $ε$ expansion, but uses the functional renormalization group, formulated directly in $d=3$ spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in $d=4$. We find new, potentially infrared stable fixed points spanned throughout the entire $N_f$ range. By conjecturing that the thermal chiral transition is governed by these ``flavor continuous" fixed points, stability analyses show that for $N_f\geq 5$ the chiral transition is of second-order, while for $N_f=2,3,4$, it is of first-order. We argue that the $U_{\rm A}(1)$ anomaly controls the strength of the first-order chiral transition for $N_f=2,3,4$, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the $U_{\rm A}(1)$ symmetry breaking around the critical temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group Fejos, G. Hatsuda, T. High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory Renormalization group flows of the $SU(N_f)\times SU(N_f)$ symmetric Ginzburg-Landau potential are calculated for a general number of flavors, $N_f$. Our approach does not rely on the $ε$ expansion, but uses the functional renormalization group, formulated directly in $d=3$ spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in $d=4$. We find new, potentially infrared stable fixed points spanned throughout the entire $N_f$ range. By conjecturing that the thermal chiral transition is governed by these ``flavor continuous" fixed points, stability analyses show that for $N_f\geq 5$ the chiral transition is of second-order, while for $N_f=2,3,4$, it is of first-order. We argue that the $U_{\rm A}(1)$ anomaly controls the strength of the first-order chiral transition for $N_f=2,3,4$, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the $U_{\rm A}(1)$ symmetry breaking around the critical temperature. |
| title | Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice High Energy Physics - Theory Nuclear Theory |
| url | https://arxiv.org/abs/2404.00554 |