- 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

Higher-derivative N=1 and N=2 supersymmetric Maxwell-Chern-Simons theories at one loop in superspace

F. S. Gama*

  • *Contact author: fgama@unifap.br
PDF

Phys. Rev. D 113, 125034 – Published 29 June, 2026

DOI: https://doi.org/10.1103/p78d-1n2n

Abstract

We define a higher-derivative generalization of N=1 and N=2 supersymmetric Maxwell-Chern-Simons theories. In particular, the chosen higher-derivative operator is a polynomial function of the d’Alembertian of arbitrary degree, and it is introduced exclusively in the gauge sector. The main goal is to explicitly compute the one-loop quantum corrections to the superfield effective potential for these theories. This is carried out by means of background field quantization in a higher-derivative Rξ gauge. The effective potential is obtained in closed form and expressed in terms of the roots of polynomial functions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. W. Siegel, Nucl. Phys. B156, 135 (1979).
  2. J. F. Schonfeld, Nucl. Phys. 185B, 157 (1981).
  3. R. Jackiw and S. Templeton, Phys. Rev. D 23, 2291 (1981).
  4. P. K. Townsend, K. Pilch, and P. van Nieuwenhuizen, Phys. Lett. 136B, 38 (1984).
  5. S. Deser and R. Jackiw, Phys. Lett. 139B, 371 (1984).
  6. O. F. Dayi, Phys. Lett. B 560, 239 (2003); M. Botta Cantcheff and P. Minces, Eur. Phys. J. C 34, 393 (2004); T. Mariz, R. Menezes, J. R. S. Nascimento, R. F. Ribeiro, and C. Wotzasek, Phys. Rev. D 70, 085018 (2004); S. Ghosh, Phys. Lett. B 583, 347 (2004).
  7. M. A. Anacleto, C. Furtado, J. R. Nascimento, and A. Yu. Petrov, Phys. Rev. D 78, 065014 (2008); A. P. Baeta Scarpelli, R. F. Ribeiro, J. R. Nascimento, and A. Yu. Petrov, Eur. Phys. J. C 75, 314 (2015); F. M. Belchior and R. V. Maluf, Phys. Lett. B 855, 138794 (2024); M. A. Anacleto, F. A. Brito, and E. Passos, Eur. Phys. J. Plus 140, 21 (2025).
  8. A. Karlhede, U. Lindstrom, M. Rocek, and P. van Nieuwenhuizen, Classical Quantum Gravity 4, 549 (1987); A. F. Ferrari, M. Gomes, J. R. S. Nascimento, A. Yu. Petrov, and A. J. da Silva, Phys. Rev. D 73, 105010 (2006); A. F. Ferrari, M. Gomes, A. C. Lehum, J. R. Nascimento, A. Yu. Petrov, and A. J. da Silva, Phys. Lett. B 678, 233 (2009); F. S. Gama, J. R. Nascimento, A. Yu. Petrov, and P. Porfirio, 868, 139727 (2025).
  9. L. Modesto, T. de Paula Netto, and I. L. Shapiro, J. High Energy Phys. 04 (2015) 098; B. L. Giacchini, Phys. Lett. B 766, 306 (2017); B. L. Giacchini and T. de Paula Netto, Eur. Phys. J. C 79, 217 (2019); J. Cosmol. Astropart. Phys. 07 (2019) 013.
  10. K. S. Stelle, Phys. Rev. D 16, 953 (1977); L. Modesto and I. L. Shapiro, Phys. Lett. B 755, 279 (2016); L. Modesto, Nucl. Phys. B909, 584 (2016); D. Anselmi, J. High Energy Phys. 06 (2017) 086; D. Anselmi and M. Piva, 05 (2018) 027.
  11. O. V. Haneychuk and K. V. Stepanyantz, Eur. Phys. J. C 85, 540 (2025); I. L. Buchbinder, A. S. Budekhina, E. A. Ivanov, and K. V. Stepanyantz, Phys. Rev. D 111, 125014 (2025); V. Yu. Shirokova and I. E. Shirokov, Phys. Part. Nucl. Lett. 22, 1351 (2025); A. Lakhal and K. Stepanyantz, Eur. Phys. J. C 86, 313 (2026).
  12. I. L. Shapiro, Classical Quantum Gravity 25, 103001 (2008).
  13. J. Scherk and J. H. Schwarz, Nucl. Phys. B81, 118 (1974); P. Candelas, G. T. Horowitz, A. Strominger, and E. Witten, B258, 46 (1985); B. Zwiebach, Phys. Lett. 156B, 315 (1985).
  14. A. R. Solomon and M. Trodden, J. Cosmol. Astropart. Phys. 02 (2018) 031; D. Glavan, J. High Energy Phys. 02 (2018) 136.
  15. A. Dutra and M. Hott, arXiv:hep-th/9403167; S. Deser and R. Jackiw, Phys. Lett. B 451, 73 (1999); S. C. Sararu, Eur. Phys. J. C 75, 526 (2015); L. H. C. Borges, F. A. Barone, and H. L. Oliveira, Phys. Rev. D 105, 025008 (2022); L. Lisboa-Santos, J. A. A. S. Reis, M. Schreck, and M. M. Ferreira, 108, 115032 (2023);
  16. B. Paul, H. Dhar, and B. Saha, Phys. Lett. B 808, 135671 (2020).
  17. R. Avila, J. R. Nascimento, A. Yu. Petrov, C. M. Reyes, and M. Schreck, Phys. Rev. D 101, 055011 (2020).
  18. P. Mukherjee and B. Paul, Phys. Rev. D 85, 045028 (2012).
  19. F. S. Gama, J. R. Nascimento, and A. Yu. Petrov, Phys. Rev. D 88, 045021 (2013).
  20. F. S. Gama, M. Gomes, J. R. Nascimento, A. Yu. Petrov, and A. J. da Silva, Phys. Rev. D 89, 085018 (2014).
  21. S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
  22. D. A. Kirzhnits and A. D. Linde, Phys. Lett. 42B, 471 (1972); S. Weinberg, Phys. Rev. D 9, 3357 (1974); L. Dolan and R. Jackiw, 9, 3320 (1974); C. W. Bernard, 9, 3312 (1974).
  23. S. R. Coleman, Phys. Rev. D 15, 2929 (1977); C. G. Callan and S. Coleman, 16, 1762 (1977); E. J. Weinberg, 47, 4614 (1993).
  24. S. J. Gates, M. T. Grisaru, M. Rocek, and W. Siegel, Front. Phys. 58, 1 (1983).
  25. J. Honerkamp, M. Schlindwein, F. Krause, and M. Scheunert, Nucl. Phys. B95, 397 (1975).
  26. M. T. Grisaru, W. Siegel, and M. Rocek, Nucl. Phys. B159, 429 (1979).
  27. A. F. Ferrari, M. Gomes, A. C. Lehum, J. R. Nascimento, A. Y. Petrov, E. O. Silva, and A. J. da Silva, Phys. Lett. B 678, 500 (2009).
  28. F. S. Gama, J. R. Nascimento, and A. Yu. Petrov, Phys. Rev. D 101, 105018 (2020).
  29. L. V. Ahlfors, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd ed. (McGraw-Hill, Inc., New York, 1979).
  30. B. M. Zupnik and D. G. Pak, Theor. Math. Phys. 77, 1070 (1988); Sov. Phys. J. 32, 962 (1988); E. A. Ivanov, Phys. Lett. B 268, 203 (1991); S. J. Gates, Jr. and H. Nishino, 281, 72 (1992); Int. J. Mod. Phys. A 08, 3371 (1993).
  31. I. L. Buchbinder, S. M. Kuzenko, and J. V. Yarevskaya, Nucl. Phys. B411, 665 (1994); Phys. At. Nucl. 56, 680 (1993).
  32. F. S. Gama, Phys. Rev. D 107, 125007 (2023).
  33. I. L. Buchbinder, B. S. Merzlikin, and I. B. Samsonov, Nucl. Phys. B860, 87 (2012).
  34. S. Axler, Linear Algebra Done Right, 4th ed. (Springer, Cham, 2024).
  35. N. K. Nielsen, Nucl. Phys. B101, 173 (1975); R. Fukuda and T. Kugo, Phys. Rev. D 13, 3469 (1976).

Outline

Information

Phys. Rev. D 113, 125034– Published 29 June, 2026
  • Received 11 May 2026
  • Accepted 9 June 2026
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