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  • Letter
  • Open Access

Constraints on the Dirac spectrum from chiral symmetry restoration

Matteo Giordano*

  • *Contact author: giordano@bodri.elte.hu
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Phys. Rev. D 110, L091504 – Published 27 November, 2024

DOI: https://doi.org/10.1103/PhysRevD.110.L091504

Abstract

I derive constraints on the Dirac spectrum in the chirally symmetric phase of a gauge theory with two massless fermion flavors. Using only general properties of correlation functions of scalar and pseudoscalar bilinears, I prove that in the chiral limit of vanishing fermion mass m the corresponding susceptibilities and all their derivatives with respect to m2 must be finite. I then use the resulting spectral constraints to show that effective breaking of the anomalous U(1)A symmetry is allowed in the SU(2)A symmetric phase in the chiral limit, and leads to distinctive spectral features: (i) the spectral density must develop a singular O(m4)/λ peak as m→0, (ii) the two-point eigenvalue correlator of near-zero modes must be singular, and (iii) near-zero modes cannot be localized. Moreover, in the symmetric phase the topological charge distribution must be indistinguishable from that of an ideal gas of instantons and anti-instantons of vanishing density, to leading order in m.

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References (58)

  1. R. D. Pisarski and F. Wilczek, Phys. Rev. D 29, 338 (1984).
  2. A. Pelissetto and E. Vicari, Phys. Rev. D 88, 105018 (2013).
  3. E. V. Shuryak, Comments Nucl. Part. Phys. 21, 235 (1994).
  4. J. I. Kapusta, D. Kharzeev, and L. D. McLerran, Phys. Rev. D 53, 5028 (1996).
  5. Z. Huang and X.-N. Wang, Phys. Rev. D 53, 5034 (1996).
  6. S. D. Bass and P. Moskal, Rev. Mod. Phys. 91, 015003 (2019).
  7. C. Bonati, M. D’Elia, M. Mariti, G. Martinelli, M. Mesiti, F. Negro, F. Sanfilippo, and G. Villadoro, J. High Energy Phys. 03 (2016) 155.
  8. P. Petreczky, H.-P. Schadler, and S. Sharma, Phys. Lett. B 762, 498 (2016).
  9. S. Borsányi et al., Nature (London) 539, 69 (2016).
  10. A. Athenodorou, C. Bonanno, C. Bonati, G. Clemente, F. D’Angelo, M. D’Elia, L. Maio, G. Martinelli, F. Sanfilippo, and A. Todaro, J. High Energy Phys. 10 (2022) 197.
  11. T. D. Cohen, Phys. Rev. D 54, R1867 (1996).
  12. S. Aoki, H. Fukaya, and Y. Taniguchi, Phys. Rev. D 86, 114512 (2012).
  13. T. Kanazawa and N. Yamamoto, J. High Energy Phys. 01 (2016) 141.
  14. N. J. Evans, S. D. H. Hsu, and M. Schwetz, Phys. Lett. B 375, 262 (1996).
  15. S. H. Lee and T. Hatsuda, Phys. Rev. D 54, R1871 (1996).
  16. T. Kanazawa and N. Yamamoto, Phys. Rev. D 91, 105015 (2015).
  17. V. Azcoiti, Phys. Rev. D 107, 114516 (2023).
  18. V. Azcoiti, Symmetry 13, 209 (2021).
  19. 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).
  20. B. B. Brandt, A. Francis, H. B. Meyer, O. Philipsen, D. Robaina, and H. Wittig, J. High Energy Phys. 12 (2016) 158.
  21. S. Aoki, Y. Aoki, G. Cossu, H. Fukaya, S. Hashimoto, T. Kaneko, C. Rohrhofer, and K. Suzuki (JLQCD Collaboration), Phys. Rev. D 103, 074506 (2021).
  22. A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 86, 094503 (2012).
  23. M. I. Buchoff et al., Phys. Rev. D 89, 054514 (2014).
  24. R. G. Edwards, U. M. Heller, J. E. Kiskis, and R. Narayanan, Phys. Rev. D 61, 074504 (2000).
  25. G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, H. Matsufuru, and J.-I. Noaki, Phys. Rev. D 87, 114514 (2013); 88, 019901(E) (2013).
  26. V. Dick, F. Karsch, E. Laermann, S. Mukherjee, and S. Sharma, Phys. Rev. D 91, 094504 (2015).
  27. A. Alexandru and I. Horváth, Phys. Rev. D 92, 045038 (2015).
  28. A. Alexandru and I. Horváth, Phys. Rev. D 100, 094507 (2019).
  29. A. Alexandru and I. Horváth, Phys. Rev. Lett. 127, 052303 (2021).
  30. A. Alexandru and I. Horváth, Phys. Lett. B 833, 137370 (2022).
  31. X.-L. Meng, P. Sun, A. Alexandru, I. Horváth, K.-F. Liu, G. Wang, and Y.-B. Yang (χQCD and CLQCD Collaborations), arXiv:2305.09459.
  32. T. G. Kovács and R. Á. Vig, Phys. Rev. D 97, 014502 (2018).
  33. R. Á. Vig and T. G. Kovács, Phys. Rev. D 103, 114510 (2021).
  34. H. T. Ding, S. T. Li, S. Mukherjee, A. Tomiya, X. D. Wang, and Y. Zhang, Phys. Rev. Lett. 126, 082001 (2021).
  35. O. Kaczmarek, L. Mazur, and S. Sharma, Phys. Rev. D 104, 094518 (2021).
  36. O. Kaczmarek, R. Shanker, and S. Sharma, Phys. Rev. D 108, 094501 (2023).
  37. A. Alexandru, C. Bonanno, M. D’Elia, and I. Horváth, Phys. Rev. D 110, 074515 (2024).
  38. T. G. Kovács, Phys. Rev. Lett. 132, 131902 (2024).
  39. N. Carabba and E. Meggiolaro, Phys. Rev. D 105, 054034 (2022).
  40. H.-T. Ding, W.-P. Huang, S. Mukherjee, and P. Petreczky, Phys. Rev. Lett. 131, 161903 (2023).
  41. M. Giordano, J. Phys. A 54, 37LT01 (2021).
  42. M. Giordano, J. High Energy Phys. 12 (2022) 103.
  43. P. H. Ginsparg and K. G. Wilson, Phys. Rev. D 25, 2649 (1982).
  44. D. B. Kaplan, Phys. Lett. B 288, 342 (1992).
  45. H. Neuberger, Phys. Lett. B 417, 141 (1998).
  46. P. Hasenfratz, Nucl. Phys. B525, 401 (1998).
  47. M. Lüscher, Phys. Lett. B 428, 342 (1998).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevD.110.L091504 for details on technical assumptions and proofs of the main statements.
  49. M. Giordano, Phys. Rev. D 107, 114509 (2023).
  50. T. Blum, N. H. Christ, C. Cristian, C. Dawson, X. Liao, G. Liu, R. Mawhinney, L. Wu, and Y. Zhestkov, Phys. Rev. D 65, 014504 (2002).
  51. M. Giordano and T. G. Kovács, Universe 7, 194 (2021).
  52. T. Guhr, A. Müller-Groeling, and H. A. Weidenmüller, Phys. Rep. 299, 189 (1998).
  53. P. Hasenfratz, V. Laliena, and F. Niedermayer, Phys. Lett. B 427, 125 (1998).
  54. M. Lüscher, Phys. Lett. B 593, 296 (2004).
  55. E. Vicari and H. Panagopoulos, Phys. Rep. 470, 93 (2009).
  56. C. Bonati, M. D’Elia, H. Panagopoulos, and E. Vicari, Phys. Rev. Lett. 110, 252003 (2013).
  57. D. J. Gross, R. D. Pisarski, and L. G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).
  58. A. Boccaletti and D. Nógrádi, J. High Energy Phys. 03 (2020) 045.

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Phys. Rev. D 110, L091504– Published 27 November, 2024
  • Received 17 April 2024
  • Accepted 7 November 2024
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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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