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  • Letter
  • Open Access

Asymptotic freedom in (3+1)-dimensional projectable Hořava gravity: Connecting the ultraviolet and infrared domains

Andrei O. Barvinsky1,2, Alexander V. Kurov1, and Sergey M. Sibiryakov3,4

  • 1Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow 117924, Russia
  • 2Institute for Theoretical and Mathematical Physics, Moscow State University, Leninskie Gory, GSP-1, Moscow, 119991, Russia
  • 3Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
  • 4Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

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Phys. Rev. D 108, L121503 – Published 18 December, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L121503

Abstract

We investigate the renormalization group flow of projectable Hořava gravity in (3+1) dimensions generated by marginal operators with respect to the Lifshitz scaling. The flow possesses a number of asymptotically free fixed points. We find a family of trajectories connecting one of these fixed points in the ultraviolet to the region of the parameter space where the kinetic term of the theory acquires the general relativistic form. The gravitational coupling exhibits nonmonotonic behavior along the flow, vanishing both in the ultraviolet and the infrared.

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References (25)

  1. P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79, 084008 (2009).
  2. K. S. Stelle, Renormalization of higher derivative quantum gravity, Phys. Rev. D 16, 953 (1977).
  3. K. S. Stelle, Classical gravity with higher derivatives, Gen. Relativ. Gravit. 9, 353 (1978).
  4. D. Blas, O. Pujolas, and S. Sibiryakov, Consistent extension of Hořava gravity, Phys. Rev. Lett. 104, 181302 (2010).
  5. D. Blas and E. Lim, Phenomenology of theories of gravity without Lorentz invariance: The preferred frame case, Int. J. Mod. Phys. D 23, 1443009 (2015).
  6. A. Emir Gümrükçüoğlu, M. Saravani, and T. P. Sotiriou, Hořava gravity after GW170817, Phys. Rev. D 97, 024032 (2018).
  7. J. Bellorín, C. Bórquez, and B. Droguett, Cancellation of divergences in the nonprojectable hořava theory, Phys. Rev. D 106, 044055 (2022).
  8. J. Bellorín, C. Bórquez, and B. Droguett, BRST symmetry and unitarity of the Hořava theory, Phys. Rev. D 107, 044059 (2023).
  9. A. O. Barvinsky, D. Blas, M. Herrero-Valea, S. M. Sibiryakov, and C. F. Steinwachs, Renormalization of Hořava gravity, Phys. Rev. D 93, 064022 (2016).
  10. A. O. Barvinsky, D. Blas, M. Herrero-Valea, S. M. Sibiryakov, and C. F. Steinwachs, Renormalization of gauge theories in the background-field approach, J. High Energy Phys. 07 (2018) 035.
  11. A. O. Barvinsky, D. Blas, M. Herrero-Valea, S. M. Sibiryakov, and C. F. Steinwachs, Hořava gravity is asymptotically free in 2+1 dimensions, Phys. Rev. Lett. 119, 211301 (2017).
  12. A. O. Barvinsky, M. Herrero-Valea, and S. M. Sibiryakov, Towards the renormalization group flow of Hořava gravity in (3+1) dimensions, Phys. Rev. D 100, 026012 (2019).
  13. A. O. Barvinsky, A. V. Kurov, and S. M. Sibiryakov, Beta functions of (3+1)-dimensional projectable Hořava gravity, Phys. Rev. D 105, 044009 (2022).
  14. A. E. Gümrükçüoğlu and S. Mukohyama, Hořava-Lifshitz gravity with λ→∞, Phys. Rev. D 83, 124033 (2011).
  15. J. I. Radkovski and S. M. Sibiryakov, Scattering amplitudes in high-energy limit of projectable Hořava gravity, Phys. Rev. D 108, 046017 (2023).
  16. K. Koyama and F. Arroja, Pathological behaviour of the scalar graviton in Hořava-Lifshitz gravity, J. High Energy Phys. 03 (2010) 061.
  17. D. Blas, O. Pujolas, and S. Sibiryakov, Models of nonrelativistic quantum gravity: The good, the bad and the healthy, J. High Energy Phys. 04 (2011) 018.
  18. S. Mukohyama, Hořava-Lifshitz cosmology: A review, Classical Quantum Gravity 27, 223101 (2010).
  19. K. Izumi and S. Mukohyama, Nonlinear superhorizon perturbations in Hořava-Lifshitz gravity, Phys. Rev. D 84, 064025 (2011).
  20. A. E. Gümrükçüoğlu, S. Mukohyama, and A. Wang, General relativity limit of Hořava-Lifshitz gravity with a scalar field in gradient expansion, Phys. Rev. D 85, 064042 (2012).
  21. P. Horava and C. M. Melby-Thompson, General covariance in quantum gravity at a Lifshitz point, Phys. Rev. D 82, 064027 (2010).
  22. A. M. da Silva, An alternative approach for general covariant Horava-Lifshitz gravity and matter coupling, Classical Quantum Gravity 28, 055011 (2011).
  23. M. Chaichian, J. Kluson, and M. Oksanen, Nonprojectable Horava-Lifshitz gravity without the unwanted scalar graviton, Phys. Rev. D 92, 104043 (2015).
  24. T. P. Sotiriou, M. Visser, and S. Weinfurtner, Phenomenologically viable Lorentz-violating quantum gravity, Phys. Rev. Lett. 102, 251601 (2009).
  25. A. O. Barvinsky, A. V. Kurov, and S. M. Sibiryakov (to be published).

Outline

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Phys. Rev. D 108, L121503– Published 18 December, 2023
  • Received 13 October 2023
  • Accepted 17 November 2023
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