- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Symmetries and anomalies of Hamiltonian staggered fermions

Simon Catterall*, Arnab Pradhan†, and Abhishek Samlodia‡

  • *Contact author: smcatter@syr.edu
  • †Contact author: arpradha@syr.edu
  • ‡Contact author: asamlodi@syr.edu
PDF

Phys. Rev. D 113, 014504 – Published 20 January, 2026

DOI: https://doi.org/10.1103/fk62-x1k3

Abstract

We review the shift (translation) and time reversal symmetries of Hamiltonian staggered fermions and their connection to continuum symmetries concentrating in particular on the case of massless fermions and (3+1) dimensions. We construct operators using the staggered fields that implement these symmetries on finite lattices. We show that shifts composed of an odd multiple of the elementary shift anticommute with time reversal and are related to continuum axial transformations. We argue that the presence of these nontrivial commutation relations implies the existence of lattice ’t Hooft anomalies. From the shifts we also construct a set of conserved, quantized charges that generate continuous symmetries of the lattice theory. In general these do not commute with the vector charge signaling further ’t Hooft anomalies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. F. Gliozzi, Nucl. Phys. B204, 419 (1982).
  2. C. van den Doel and J. Smit, Nucl. Phys. B228, 122 (1983).
  3. M. F. L. Golterman and J. Smit, Nucl. Phys. B245, 61 (1984).
  4. H. Sharatchandra, H. Thun, and P. Weisz, Nucl. Phys. B192, 205 (1981).
  5. H. Kluberg-Stern, A. Morel, O. Napoly, and B. Petersson, Nucl. Phys. B220, 447 (1983).
  6. G. W. Kilcup and S. R. Sharpe, Nucl. Phys. B283, 493 (1987).
  7. L. Susskind, Phys. Rev. D 16, 3031 (1977).
  8. R. Dempsey, I. R. Klebanov, S. S. Pufu, and B. Zan, Phys. Rev. Res. 4, 043133 (2022).
  9. A. Chatterjee, S. D. Pace, and S.-H. Shao, Phys. Rev. Lett. 134, 021601 (2025).
  10. N. Butt, S. Catterall, A. Pradhan, and G. C. Toga, Phys. Rev. D 104, 094504 (2021).
  11. S. Catterall, Phys. Rev. D 107, 014501 (2023).
  12. S. Catterall and A. Pradhan, Phys. Rev. D 110, 094516 (2024).
  13. M. Cheng and N. Seiberg, SciPost Phys. 15, 051 (2023).
  14. N. Seiberg and S.-H. Shao, SciPost Phys. 16, 064 (2024).
  15. M. Nguyen and H. Singh, Phys. Rev. D 107, 014507 (2023).
  16. V. Ayyar and S. Chandrasekharan, Phys. Rev. D 91, 065035 (2015).
  17. V. Ayyar and S. Chandrasekharan, J. High Energy Phys. 10 (2016) 058.
  18. S. Catterall, J. High Energy Phys. 01 (2016) 121.
  19. J. Wang and Y.-Z. You, Symmetry 14, 1475 (2022).
  20. M. Zeng, Z. Zhu, J. Wang, and Y.-Z. You, Phys. Rev. Lett. 128, 185301 (2022).
  21. S. Catterall, SciPost Phys. 16, 108 (2024).
  22. J. B. Kogut and L. Susskind, Phys. Rev. D 11, 395 (1975).
  23. W. Bock, J. Smit, and J. C. Vink, Phys. Lett. B 291, 297 (1992).
  24. E. Kahler, Rend. Math. 3–4 21, 425 (1962).
  25. D. Iwanenko and L. Landau, Z. Phys. 48, 340 (1928).
  26. E. Poppitz and Y. Shang, Int. J. Mod. Phys. A 25, 2761 (2010).
  27. Y.-Z. You and C. Xu, Phys. Rev. B 91, 125147 (2015).
  28. L. Fidkowski and A. Kitaev, Phys. Rev. B 81, 134509 (2010).
  29. V. Ayyar and S. Chandrasekharan, Phys. Rev. D 93, 081701 (2016).
  30. N. Butt, S. Catterall, and G. C. Toga, Symmetry 13, 2276 (2021).
  31. S. Catterall and D. Schaich, Phys. Rev. D 96, 034506 (2017).
  32. N. Butt, S. Catterall, and D. Schaich, Phys. Rev. D 98, 114514 (2018).
  33. S. S. Razamat and D. Tong, Phys. Rev. X 11, 011063 (2021).
  34. J. Wang and X.-G. Wen, Phys. Rev. Res. 2, 023356 (2020).
  35. I. García-Etxebarria and M. Montero, J. High Energy Phys. 08 (2019) 003.
  36. E. Witten, Rev. Mod. Phys. 88, 035001 (2016).
  37. Y.-Y. Li, J. Wang, and Y.-Z. You, arXiv:2412.19691.
  38. M. Golterman, arXiv:2406.02906.

Outline

Information

Phys. Rev. D 113, 014504– Published 20 January, 2026
  • Received 25 April 2025
  • Accepted 22 December 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation