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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

Hidenori Fukaya

  • Fundamental Quantum Science Program (FQSP), TRIP Headquarter, RIKEN Hirosawa 2-1, Wako, Saitama 351-0198, Japan and Yukawa Institute for Theoretical Physics (YITP), Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan

  • Department of physics, The University of Osaka, Toyonaka 560-0043, Japan

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Phys. Rev. D 114, 018502 – Published 21 July, 2026

DOI: https://doi.org/10.1103/dk71-9mzv

Abstract

We respond to the comment by Matteo Giordano [1] on our article [2]. We find—and [1] itself acknowledges—that the proposed counterexamples intended to refute our argument violate a crucial assumption of QCD at high temperatures, namely that every gluonic observable is an analytic function of the squared quark mass, m2. We further point out a technical mistake found in [1]. We conclude that the arguments presented in [1] are not valid.

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Comments & Replies

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

Matteo Giordano
Phys. Rev. D 114, 018501 (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 (2)

  1. Matteo Giordano, preceding Comment, Comment on “Chiral symmetry restoration, the eigenvalue density of the Dirac operator, and the axial U(1) anomaly at finite temperature”, Phys. Rev. D 114, 018501 (2026).
  2. S. Aoki, H. Fukaya, and Y. Taniguchi, Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature, Phys. Rev. D 86, 114512 (2012).

Outline

Information

Phys. Rev. D 114, 018502– Published 21 July, 2026
  • Received 28 April 2026
  • 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.

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