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Comment on “Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature”

Matteo Giordano*

  • *Contact author: giordano@bodri.elte.hu
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Phys. Rev. D 114, 018501 – Published 21 July, 2026

DOI: https://doi.org/10.1103/xs2n-c7t9

Abstract

Aoki, Fukaya, and Taniguchi claim that both the spectral density of the Dirac operator at the origin and the topological susceptibility must vanish identically for sufficiently small but nonzero quark mass m in the chirally symmetric phase of quantum chromodynamics with two light quark flavors, under certain technical assumptions on the spectrum and on the dependence of observables on m. I argue that a crucial step of their proof is not justified and the validity of these conclusions should be reassessed.

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Comments & Replies

Reply to “Comment on ‘Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature”’

Sinya Aoki and Hidenori Fukaya
Phys. Rev. D 114, 018502 (2026)

Article Text

Original Article

Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature

Sinya Aoki, Hidenori Fukaya, and Yusuke Taniguchi
Phys. Rev. D 86, 114512 (2012)

References (11)

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  3. A. Tomiya, G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, and J. Noaki, Phys. Rev. D 96, 034509 (2017); 96, 079902(A) (2017).
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  5. S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, I. Kanamori, T. Kaneko, Y. Nakamura, C. Rohrhofer, K. Suzuki, and D. Ward (JLQCD collaboration), Proc. Sci., LATTICE2023 (2024) 185 [arXiv:2401.14022].
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  8. H.-T. Ding et al. (HotQCD Collaboration), Phys. Rev. Lett. 123, 062002 (2019).
  9. H. T. Ding, S. T. Li, S. Mukherjee, A. Tomiya, X. D. Wang, and Y. Zhang, Phys. Rev. Lett. 126, 082001 (2021).
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  11. M. Giordano, arXiv:2510.24381.

Outline

Information

Phys. Rev. D 114, 018501– Published 21 July, 2026
  • Received 14 November 2025
  • Accepted 22 May 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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