- 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

Quasitopological mass generation for 3D linearized gravity

Erica Bertolini1,*, Edoardo Lui2,†, and Nicola Maggiore2,3,‡

  • *Contact author: ebertolini@stp.dias.ie
  • †Contact author: edoardo.lui@gmail.com
  • ‡Contact author: nicola.maggiore@ge.infn.it
PDF

Phys. Rev. D 112, 044035 – Published 19 August, 2025

DOI: https://doi.org/10.1103/db71-jwd2

Abstract

We present a new mass generation mechanism for linearized gravity in three spacetime dimensions, which consists of a lower-dimensional Chern-Simons-like term added to the invariant action. The propagators of the gauge-fixed massive action show a massive pole and a good massless limit. Moreover, we show that, as the topological massive gravity model of Deser, Jackiw, and Templeton, this theory displays one propagating massive degree of freedom, which can be traced back to the transverse part of the spatial Ricci tensor. Finally, the action of this linearized massive gravity is characterized by an algebraic structure formed by a set of Ward operators, which uniquely determine the theory.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (30)

  1. E. Witten, Three-dimensional gravity revisited, arXiv:0706.3359.
  2. S. Deser, R. Jackiw, and S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48, 975 (1982).
  3. S. Deser, R. Jackiw, and S. Templeton, Topologically massive gauge theories, Ann. Phys. (N.Y.) 140, 372 (1982); 185, 406(E) (1988).
  4. E. A. Bergshoeff, O. Hohm, and P. K. Townsend, Massive gravity in three dimensions, Phys. Rev. Lett. 102, 201301 (2009).
  5. D. Dalmazi and R. R. L. d. Santos, The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms, Eur. Phys. J. C 81, 547 (2021).
  6. M. Pretko, X. Chen, and Y. You, Fracton phases of matter, Int. J. Mod. Phys. A 35, 2030003 (2020).
  7. M. Pretko, The fracton gauge principle, Phys. Rev. B 98, 115134 (2018).
  8. E. Bertolini, A. Blasi, N. Maggiore, and D. S. Shaikh, Hall-like behaviour of higher rank Chern-Simons theory of fractons, J. High Energy Phys. 10 (2024) 232.
  9. E. Bertolini, A. Blasi, and N. Maggiore, Quasi-topological fractons: A 3D dipolar gauge theory, Eur. Phys. J. C 85, 68 (2025).
  10. E. Bertolini and N. Maggiore, Maxwell theory of fractons, Phys. Rev. D 106, 125008 (2022).
  11. C. Aragone and A. Khoudeir, Selfdual massive gravity, Phys. Lett. B 173, 141 (1986).
  12. D. Dalmazi and E. L. Mendonca, A new spin-2 self-dual model in D=2+1, J. High Energy Phys. 09 (2009) 011.
  13. D. Dalmazi and A. L. R. d. Santos, Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity, Phys. Rev. D 104, 085023 (2021).
  14. S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Cambridge University Press, Cambridge, England, 2019).
  15. M. Blau, Lecture notes on general relativity, http://blau.itp.unibe.ch/GRLecturenotes.html.
  16. C. Itzykson and J. B. Zuber, Quantum Field Theory (Dover Publications, New York, 2012).
  17. K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84, 671 (2012).
  18. A. Blasi and N. Maggiore, Massive gravity and Fierz-Pauli theory, Eur. Phys. J. C 77, 614 (2017).
  19. A. Blasi and N. Maggiore, Massive deformations of rank-2 symmetric tensor theory (a.k.a. BRS characterization of Fierz–Pauli massive gravity), Classical Quantum Gravity 34, 015005 (2017).
  20. G. Gambuti and N. Maggiore, A note on harmonic gauge(s) in massive gravity, Phys. Lett. B 807, 135530 (2020).
  21. G. Gambuti and N. Maggiore, Fierz–Pauli theory reloaded: From a theory of a symmetric tensor field to linearized massive gravity, Eur. Phys. J. C 81, 171 (2021).
  22. C. Becchi, A. Rouet, and R. Stora, Renormalization of gauge theories, Ann. Phys. (N.Y.) 98, 287 (1976).
  23. R. Stora, Continuum gauge theories, Conf. Proc. C 7607121, 201 (1976).
  24. N. Nakanishi, Covariant quantization of the electromagnetic field in the Landau gauge, Prog. Theor. Phys. 35, 1111 (1966).
  25. B. Lautrup, Canonical quantum electrodynamics in covariant gauges, Kong. Dan. Vid. Sel. Mat. Fys. Med. 35, 11 (1967).
  26. M. Nakasone and I. Oda, Massive gravity with mass term in three dimensions, Phys. Rev. D 79, 104012 (2009).
  27. A. Accioly, J. Helayel-Neto, B. Pereira-Dias, and C. Hernaski, A new class of spin projection operators for 3D models, Phys. Rev. D 86, 105046 (2012).
  28. M. Nakasone and I. Oda, On unitarity of massive gravity in three dimensions, Prog. Theor. Phys. 121, 1389 (2009).
  29. H. van Dam and M. J. G. Veltman, Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B22, 397 (1970).
  30. V. I. Zakharov, Linearized gravitation theory and the graviton mass, JETP Lett. 12, 312 (1970).

Outline

Information

Phys. Rev. D 112, 044035– Published 19 August, 2025
  • Received 18 April 2025
  • Accepted 28 July 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