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Studying QED3 with radial quantization on the lattice: Free limit

Peter A. Boyle1, Richard C. Brower2, George T. Fleming3, Emanuel Katz2, Nobuyuki Matsumoto2,*, and Rohan Misra2

  • *Contact author: nmatsum@bu.edu
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Phys. Rev. D 112, 114514 – Published 26 December, 2025

DOI: https://doi.org/10.1103/jwkk-q8nt

Abstract

To investigate the three-dimensional quantum electrodynamics in the radial quantization on the lattice, the lattice action is constructed and the free limit is studied on S2×R. With the overlap fermion, it is numerically verified that the important symmetries of the theory can be realized on the lattice. The analytic correlators are derived and compared to the lattice results, which agree including the overall normalization. The O(a2) scaling is confirmed toward the analytic value in the continuum limit, and the number of reproduced excited states is estimated heuristically for the first few refinement levels. Our study helps us identify the features of the theory that we can study on the icosahedral lattice without fine-tuning.

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References (82)

  1. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, Nucl. Phys. B241, 333 (1984).
  2. F. Gross et al., Eur. Phys. J. C 83, 1125 (2023).
  3. R. C. Brower, G. Fleming, A. Gasbarro, T. Raben, C.-I. Tan, and E. Weinberg, Proc. Sci. LATTICE2015 (2016) 296 [arXiv:1601.01367].
  4. S. Fubini, A. J. Hanson, and R. Jackiw, Phys. Rev. D 7, 1732 (1973).
  5. J. L. Cardy, J. Phys. A 17, L385 (1984).
  6. J. L. Cardy, J. Phys. A 18, L757 (1985).
  7. R. C. Brower, G. T. Fleming, and H. Neuberger, Phys. Lett. B 721, 299 (2013).
  8. R. C. Brower, M. Cheng, and G. T. Fleming, Proc. Sci. LATTICE2013 (2014) 335 [arXiv:1407.7597].
  9. R. C. Brower, G. T. Fleming, A. D. Gasbarro, D. Howarth, T. G. Raben, C.-I. Tan, and E. S. Weinberg, Phys. Rev. D 104, 094502 (2021).
  10. R. C. Brower et al. (Lattice Strong Dynamics Collaboration), Phys. Rev. D 110, 054501 (2024).
  11. A. Hasenfratz, Phys. Rev. D 106, 014513 (2022).
  12. N. Butt, S. Catterall, and A. Hasenfratz, Phys. Rev. Lett. 134, 031602 (2025).
  13. S. Deser, R. Jackiw, and S. Templeton, Ann. Phys. (N.Y.) 140, 372 (1982); 185, 406(E) (1988).
  14. A. N. Redlich, Phys. Rev. Lett. 52, 18 (1984).
  15. A. N. Redlich, Phys. Rev. D 29, 2366 (1984).
  16. T. Appelquist, M. J. Bowick, D. Karabali, and L. C. R. Wijewardhana, Phys. Rev. D 33, 3774 (1986).
  17. S. Albayrak, R. S. Erramilli, Z. Li, D. Poland, and Y. Xin, Phys. Rev. D 105, 085008 (2022).
  18. N. Dorey and N. Mavromatos, Phys. Lett. B 250, 107 (1990).
  19. N. Dorey and N. Mavromatos, Nucl. Phys. B386, 614 (1992).
  20. I. J. R. Aitchison, N. Dorey, M. Klein-Kreisler, and N. E. Mavromatos, Phys. Lett. B 294, 91 (1992).
  21. I. J. R. Aitchison, Z. Phys. C 67, 303 (1995).
  22. K. Farakos and N. E. Mavromatos, Mod. Phys. Lett. A 13, 1019 (1998).
  23. E. Dagotto, J. B. Kogut, and A. Kocic, Phys. Rev. Lett. 62, 1083 (1989).
  24. E. Dagotto, A. Kocic, and J. B. Kogut, Nucl. Phys. B334, 279 (1990).
  25. J. Alexandre, K. Farakos, S. J. Hands, G. Koutsoumbas, and S. E. Morrison, Phys. Rev. D 64, 034502 (2001).
  26. D. Lee and P. Maris, Phys. Rev. D 67, 076002 (2003).
  27. S. J. Hands, J. B. Kogut, and C. G. Strouthos, Nucl. Phys. B645, 321 (2002).
  28. S. J. Hands, J. B. Kogut, L. Scorzato, and C. G. Strouthos, Phys. Rev. B 70, 104501 (2004).
  29. V. Azcoiti and X.-Q. Luo, Mod. Phys. Lett. A 08, 3635 (1993).
  30. R. Fiore, P. Giudice, D. Giuliano, D. Marmottini, A. Papa, and P. Sodano, Phys. Rev. D 72, 094508 (2005); 72, 119902(E) (2005).
  31. C. Strouthos and J. B. Kogut, Proc. Sci. LATTICE2007 (2007) 278 [arXiv:0804.0300].
  32. O. Raviv, Y. Shamir, and B. Svetitsky, Phys. Rev. D 90, 014512 (2014).
  33. N. Karthik and R. Narayanan, Phys. Rev. D 93, 045020 (2016).
  34. N. Karthik and R. Narayanan, Phys. Rev. D 94, 065026 (2016).
  35. N. Karthik and R. Narayanan, Phys. Rev. D 100, 054514 (2019).
  36. N. Karthik and R. Narayanan, Phys. Rev. Lett. 125, 261601 (2020).
  37. N. H. Christ, R. Friedberg, and T. D. Lee, Nucl. Phys. B210, 310 (1982).
  38. N. H. Christ, R. Friedberg, and T. D. Lee, Nucl. Phys. B210, 337 (1982).
  39. R. Friedberg, T. D. Lee, and H.-C. Ren, Prog. Theor. Phys. Suppl. 86, 322 (1986).
  40. B.-X. Lao and S. Rychkov, SciPost Phys. 15, 243 (2023).
  41. R. D. Pisarski, Phys. Rev. D 29, 2423 (1984).
  42. T. W. Appelquist, M. J. Bowick, D. Karabali, and L. C. R. Wijewardhana, Phys. Rev. D 33, 3704 (1986).
  43. R. C. Brower, E. S. Weinberg, G. T. Fleming, A. D. Gasbarro, T. G. Raben, and C.-I. Tan, Phys. Rev. D 95, 114510 (2017).
  44. K. G. Wilson, in New Phenomena in Subnuclear Physics: Part A, edited by A. Zichichi (Plenum Press, New York and London, 1977), pp. 69–142.
  45. R. Narayanan and H. Neuberger, Nucl. Phys. B443, 305 (1995).
  46. R. Narayanan and J. Nishimura, Nucl. Phys. B508, 371 (1997).
  47. Y. Kikukawa and H. Neuberger, Nucl. Phys. B513, 735 (1998).
  48. Y. Kikukawa and A. Yamada, Phys. Lett. B 448, 265 (1999).
  49. P. H. Ginsparg and K. G. Wilson, Phys. Rev. D 25, 2649 (1982).
  50. W. Bietenholz and J. Nishimura, J. High Energy Phys. 07 (2001) 015.
  51. M. Luscher, Phys. Lett. B 428, 342 (1998).
  52. J. van den Eshof, A. Frommer, T. Lippert, K. Schilling, and H. A. van der Vorst, Comput. Phys. Commun. 146, 203 (2002).
  53. T.-W. Chiu, T.-H. Hsieh, C.-H. Huang, and T.-R. Huang, Phys. Rev. D 66, 114502 (2002).
  54. S. Elitzur, Phys. Rev. D 12, 3978 (1975).
  55. P. Boyle, G. Cossu, A. Yamaguchi, and A. Portelli, Proc. Sci. LATTICE2015 (2016) 023 [arXiv:1512.03487].
  56. F. Karsch, Nucl. Phys. B205, 285 (1982).
  57. G. Burgers, F. Karsch, A. Nakamura, and I. O. Stamatescu, Nucl. Phys. B304, 587 (1988).
  58. R. G. Edwards, B. Joo, and H.-W. Lin, Phys. Rev. D 78, 054501 (2008).
  59. H.-W. Lin et al. (Hadron Spectrum Collaboration), Phys. Rev. D 79, 034502 (2009).
  60. R. C. Brower and E. K. Owen, arXiv:2407.00459.
  61. R. C. Brower, G. T. Fleming, K. Svenson, and N. Matsumoto (to be published).
  62. W. Zhu, C. Han, E. Huffman, J. S. Hofmann, and Y.-C. He, Phys. Rev. X 13, 021009 (2023).
  63. G. Fardelli, A. L. Fitzpatrick, and E. Katz, SciPost Phys. 18, 086 (2025).
  64. A. M. Läuchli, L. Herviou, P. H. Wilhelm, and S. Rychkov, SciPost Phys. 19, 076 (2025).
  65. D. B. Kaplan, Phys. Lett. B 288, 342 (1992).
  66. Y. Shamir, Nucl. Phys. B406, 90 (1993).
  67. V. Furman and Y. Shamir, Nucl. Phys. B439, 54 (1995).
  68. H. Neuberger, Phys. Rev. D 57, 5417 (1998).
  69. S. Hands, Phys. Lett. B 754, 264 (2016).
  70. S. Hands, J. High Energy Phys. 09 (2015) 047.
  71. R. C. Brower, H. Neff, and K. Orginos, Comput. Phys. Commun. 220, 1 (2017).
  72. M. Clancy and D. B. Kaplan, Phys. Rev. D 111, L031503 (2025).
  73. D. B. Kaplan and S. Sen, arXiv:2412.02024.
  74. S. Aoki and H. Fukaya, Prog. Theor. Exp. Phys. 2023, 033B05 (2023).
  75. M. Golterman and Y. Shamir, Phys. Rev. D 109, 114519 (2024).
  76. K. Yamamoto, N. Kan, and H. Fukaya, arXiv:2507.06586.
  77. R. Frezzotti, P. A. Grassi, S. Sint, and P. Weisz (Alpha Collaboration), J. High Energy Phys. 08 (2001) 058.
  78. R. Frezzotti and G. C. Rossi, J. High Energy Phys. 08 (2004) 007.
  79. N. Matsumoto (2025), 10.5281/zenodo.17210221.
  80. https://github.com/brower/newQFE (2024).
  81. A. A. Abrikosov, Jr., arXiv:hep-th/0212134.
  82. G. Szegö, Orthogonal Polynomials (American Mathematical Society, Providence, RI, 1975).

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Phys. Rev. D 112, 114514– Published 26 December, 2025
  • Received 20 October 2025
  • Accepted 10 December 2025
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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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