Journal of High Energy Physics

, 2010:9 | Cite as

Counterterms in semiclassical Hořava-Lifshitz gravity

  • Gastón Giribet
  • Diana López Nacir
  • Francisco D. Mazzitelli


We analyze the semiclassical Hořava-Lifshitz gravity for quantum scalar fields in 3 + 1 dimensions. The renormalizability of the theory requires that the action of the scalar field contains terms with six spatial derivatives of the field, i.e. in the UV, the classical action of the scalar field should preserve the anisotropic scaling symmetry (tL 2z t, \( \vec{x} \to {L^2}\vec{x} \), with z = 3) of the gravitational action. We discuss the renormalization procedure based on adiabatic subtraction and dimensional regularization in the weak field approximation. We verify that the divergent terms in the adiabatic expansion of the expectation value of the energy-momentum tensor of the scalar field contain up to six spatial derivatives, but do not contain more than two time derivatives. We compute explicitly the counterterms needed for the renormalization of the theory up to second adiabatic order and evaluate the associated β functions in the minimal subtraction scheme.


Models of Quantum Gravity Renormalization Regularization and Renormalons 


  1. [1]
    P. Hořava, Quantum gravity at a Lifshitz point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [SPIRES].ADSGoogle Scholar
  2. [2]
    P. Hořava and C.M. Melby-Thompson, General covariance in quantum gravity at a Lifshitz point, arXiv:1007.2410 [SPIRES].
  3. [3]
    D. Blas, O. Pujolàs and S. Sibiryakov, On the extra mode and inconsistency of Hořava gravity, JHEP 10 (2009) 029 [arXiv:0906.3046] [SPIRES].ADSCrossRefGoogle Scholar
  4. [4]
    C. Charmousis, G. Niz, A. Padilla and P.M. Saffin, Strong coupling in Hořava gravity, JHEP 08 (2009) 070 [arXiv:0905.2579] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    M. Li and Y. Pang, A trouble with Hořava-Lifshitz gravity, JHEP 08 (2009) 015 [arXiv:0905.2751] [SPIRES].MathSciNetADSGoogle Scholar
  6. [6]
    M. Henneaux, A. Kleinschmidt and G.L. Gomez, A dynamical inconsistency of Hořava gravity, Phys. Rev. D 81 (2010) 064002 [arXiv:0912.0399] [SPIRES].MathSciNetADSGoogle Scholar
  7. [7]
    D. Blas, O. Pujolàs and S. Sibiryakov, Consistent extension of Hořava gravity, Phys. Rev. Lett. 104 (2010) 181302 [arXiv:0909.3525] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    D. Blas, O. Pujolàs and S. Sibiryakov, Comment on ‘Strong coupling in extended Hořava-Lifshitz gravity’, Phys. Lett. B 688 (2010) 350 [arXiv:0912.0550] [SPIRES].ADSGoogle Scholar
  9. [9]
    D. Blas, O. Pujolàs and S. Sibiryakov, Models of non-relativistic quantum gravity: the good, the bad and the healthy, arXiv:1007.3503 [SPIRES].
  10. [10]
    D. Lopez Nacir and F.D. Mazzitelli, Renormalization in theories with modified dispersion relations: weak gravitational fields, Phys. Lett. B 672 (2009) 294 [arXiv:0810.2922] [SPIRES]. ADSGoogle Scholar
  11. [11]
    T. Jacobson, Extended Hořava gravity and Einstein-aether theory, Phys. Rev. D 81 (2010) 101502 [arXiv:1001.4823] [SPIRES].ADSGoogle Scholar
  12. [12]
    C. Germani, A. Kehagias and K. Sfetsos, Relativistic quantum gravity at a Lifshitz point, JHEP 09 (2009) 060 [arXiv:0906.1201] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    X. Gao, Y. Wang, R. Brandenberger and A. Riotto, Cosmological perturbations in Hořava-Lifshitz gravity, Phys. Rev. D 81 (2010) 083508 [arXiv:0905.3821] [SPIRES].ADSGoogle Scholar
  14. [14]
    D. Anselmi and M. Halat, Renormalization of Lorentz violating theories, Phys. Rev. D 76 (2007) 125011 [arXiv:0707.2480] [SPIRES].ADSGoogle Scholar
  15. [15]
    M. Visser, Power-counting renormalizability of generalized Hořava gravity, arXiv:0912.4757 [SPIRES].
  16. [16]
    J. Collins, Renormalization, Cambridge University Press, Cambridge U.K. (1984).MATHCrossRefGoogle Scholar
  17. [17]
    N.D. Birrell and P.C.W. Davies, Quantum Fields in curved space, Cambridge University Press, Cambridge U.K. (1982).MATHGoogle Scholar
  18. [18]
    I.L. Buchbinder, S.D. Odintsov and I.L. Shapiro, Effective action in quantum gravity, Institute of Physics Publishing, U.S.A. (1992).Google Scholar
  19. [19]
    R. Iengo, J.G. Russo and M. Serone, Renormalization group in Lifshitz-type theories, JHEP 11 (2009) 020 [arXiv:0906.3477] [SPIRES].ADSCrossRefGoogle Scholar
  20. [20]
    E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space, JHEP 02 (2003) 021 [hep-ph/0210388] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  21. [21]
    D. Nesterov and S.N. Solodukhin, Gravitational effective action and entanglement entropy in UV modified theories with and without Lorentz symmetry, arXiv:1007.1246 [SPIRES].

Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Gastón Giribet
    • 1
  • Diana López Nacir
    • 1
  • Francisco D. Mazzitelli
    • 1
  1. 1.Departamento de Física, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos Aires and IFIBA, CONICET. Ciudad UniversitariaBuenos AiresArgentina

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