- 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

Covariant quantization of totally antisymmetric tensor-spinor field in AdSd

A. O. Barvinsky1,2,*, I. L. Buchbinder3,4,5,†, V. A. Krykhtin6,‡, and D. V. Nesterov1,§

  • *Contact author: barvin@lpi.ru
  • †Contact author: buchbinder@theor.jinr.ru
  • ‡Contact author: krykhtin@tpu.ru
  • §Contact author: nesterov@lpi.ru
PDF

Phys. Rev. D 113, 045022 – Published 24 February, 2026

DOI: https://doi.org/10.1103/1f2m-wg1p

Abstract

We develop the quantization of a recently proposed model describing a totally antisymmetric rank-p tensor-spinor field (a fermionic p-form theory) in d-dimensional anti–de Sitter (AdS) space. The model provides a new nontrivial example of a reducible gauge theory, in which gauge transformations are linearly dependent and the degree of reducibility increases with p. It is well-known that in such cases the standard Faddeev-Popov-DeWitt prescription for the generating functional is not applicable. We quantize the fermionic p-form theory using the general Batalin-Vilkovisky formalism, employing two distinct gauge fermions associated with gauge-fixing functions of different admissible ranks, confirming the independence from the gauge choice. As a result, we obtain the quantum effective action in terms of a sequence of functional determinants corresponding to specific Dirac-like operators on AdS space.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. C. V. Johnson, D-Branes (Cambridge University Press, Cambridge, England, 2003), p. 548.
  2. T. Ortin, Gravity and Strings (Cambridge University Press, Cambridge, England, 2004), p. 684.
  3. D. Z. Freedman and A. Van Proeyen, Supergravity (Cambridge University Press, Cambridge, England, 2012), p. 607.
  4. V. I. Ogievetsky and I. V. Polubarinov, The notoph and its possible interactions, Yad. Fiz. 4, 216 (1966).
  5. M. Kalb and P. Ramond, Classical direct interstring action, Phys. Rev. D 9, 2273 (1974).
  6. E. A. Ivanov, Gauge fields, nonlinear realizations and supersymmetry, Phys. Part. Nucl. 47, 508 (2016).
  7. D. Z. Freedman and P. K. Townsend, Antisymmetric tensor gauge fields and nonlinear sigma models, Nucl. Phys. B177, 282 (1981).
  8. I. L. Buchbinder, E. N. Kirillova, and N. G. Pletnev, Quantum equivalence of massive antisymmetric tensor field models in curved space, Phys. Rev. D 78, 084024 (2008).
  9. S. M. Kuzenko and E. S. N. Raptakis, Covariant quantisation of tensor multiplet models, J. High Energy Phys. 09 (2024) 182.
  10. A. S. Schwarz, The partition function of degenerate quadratic functionals and Ray-Singer invariants, Lett. Math. Phys. 2, 247 (1978).
  11. A. S. Schwarz, The partition function of a degenerate functional, Commun. Math. Phys. 67, 1 (1979).
  12. W. Siegel, Hidden ghosts, Phys. Lett. 93B, 170 (1980).
  13. I. L. Buchbinder and S. M. Kuzenko, Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence, Nucl. Phys. B308, 162 (1988).
  14. I. L. Buchbinder, V. A. Krykhtin, and L. L. Ryskina, Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdSd space, Nucl. Phys. B819, 453 (2009).
  15. Yu. M. Zinoviev, Note on antisymmetric spin-tensors, J. High Energy Phys. 04 (2009) 035.
  16. A. Campoleoni, D. Francia, J. Mourad, and A. Sagnotti, Unconstrained higher spins of mixed symmetry. II. Fermi fields, Nucl. Phys. B828, 405 (2010).
  17. E. D. Skvortsov and Y. M. Zinoviev, Frame-like actions for massless mixed-symmetry fields in Minkowski space. Fermions, Nucl. Phys. B843, 559 (2011).
  18. C. M. Hull, Stronly coupled gravity and dualities, Nucl. Phys. B583, 237 (2000).
  19. C. M. Hull, Symmetries and compactifications of (4, 0) conformal gravity, J. High Energy Phys. 12 (2000) 007.
  20. P. West, E(11) and M theory, Classical Quantum Gravity 18, 443 (2001).
  21. C. M. Hull, Duality in gravity and higher spin gauge fields, J. High Energy Phys. 09 (2001) 027.
  22. L. Borsten, D=6,N=(2,0) and N=(4,0) theories, Phys. Rev. D 97, 066014 (2018).
  23. M. Henneaux, V. Lekeu, and A. Leonard, The action of the (free) (4, 0)-theory, J. High Energy Phys. 01 (2018) 114; 05 (2018) 105(E).
  24. M. Henneaux, V. Lekeu, J. Matulich, and S. Prohazka, The action of the (free) N+(3,1) theory in six spacetime dimensions, J. High Energy Phys. 06 (2018) 057.
  25. R. Minasian, C. Strickland-Constable, and Y. Zhang, On symmetries and dynamics of exotic supermultiplets, J. High Energy Phys. 01 (2021) 174.
  26. Y. Bertrand, S. Hohenegger, O. Holm, and H. Samtleben, Towards exotic 6D supergravities, Phys. Rev. D 103, 046002 (2021).
  27. M. Cederwall, Superspace formulation of exotic supergravities in six dimensions, J. High Energy Phys. 03 (2021) 056.
  28. M. Gunaydin, Unified non-metric (1, 0) tensor-Einstein supergravity theories and (4, 0) supergravity in six dimensions, J. High Energy Phys. 06 (2021) 081.
  29. I. A. Batalin and G. A. Vilkovisky, Gauge algebra and quantization, Phys. Lett. 102B, 27 (1981).
  30. I. A. Batalin and G. A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28, 2567 (1983); 30, 508(E) (1984).
  31. M. Henneaux, Hamiltonian form for the path integral for theories with a gauge freedom, Phys. Rep. 126, 1 (1985).
  32. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, NJ, 1992), p. 552.
  33. J. Gomis, J. Paris, and S. Samuel, Antibracket, antifields and gauge theory quantization, Phys. Rep. 259, 1 (1995).
  34. A. Barvinsky, I. Buchbinder, V. Krykhtin, and D. Nesterov, Adjustment of Faddeev-Popov quantization to reducible gauge theories: Antisymmetric tensor fermion in AdSd space, Phys. Rev. D 112, 065021 (2025).
  35. V. Lekeu and Y. Zhang, On the quantisation and anomalies of antisymmetric tensor-spinors, J. High Energy Phys. 11 (2021) 078.
  36. R. Camporesi, Harmonic analysis, and propagators on homogeneous space, Phys. Rep. 196, 1 (1990).
  37. https://rscf.ru/en/project/23-12-00051/.
  38. A. O. Barvinsky and D. V. Nesterov, Restricted gauge theory formalism and unimodular gravity, Phys. Rev. D 108, 065004 (2023).

Outline

Information

Phys. Rev. D 113, 045022– Published 24 February, 2026
  • Received 6 September 2025
  • Accepted 24 November 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