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Flavor dependence of chiral symmetry breaking and the conformal window

Yi-huai Chen1,*, Yi Lu2,3,4,†, Zhi-wei Wang5,‡, Yu-xin Liu2,3,4,§, and Fei Gao1,∥

  • *Contact author: 3120231486@bit.edu.cn
  • †Contact author: qwertylou@pku.edu.cn
  • ‡Contact author: zhiwei.wang@uestc.edu.cn
  • §Contact author: yxliu@pku.edu.cn
  • ∥Contact author: fei.gao@bit.edu.cn
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Phys. Rev. D 114, 014065 – Published 29 July, 2026

DOI: https://doi.org/10.1103/sbyz-5gl5

Abstract

We investigate the phase structure of QCD in the vacuum as a function of quark flavor number Nf within the chiral limit. By self-consistently solving the coupled Dyson-Schwinger equations for the quark and gluon propagators in a minimal QCD scheme, we elucidate the nonperturbative dynamics governing dynamical chiral symmetry breaking. Our calculations determine a critical flavor number of Nfc=6.81 which marks the chiral symmetry restoration of quarks. Further analysis reveals the critical exponents of the chiral condensate as −⟨ψ¯ψ⟩∼|Nf−Nfc|0.53(9), characterized the second order feature of this phase transition of chiral symmetry. Additionally, we discuss the implications for the walking regime towards the conformal window at larger flavor.

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Phys. Rev. D 114, 014065– Published 29 July, 2026
  • Received 9 March 2026
  • Accepted 14 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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