Asymptotic freedom in Hořava-Lifshitz gravity.
We use the Wetterich equation for foliated spacetimes to study the renormalization group flow of projectable Hořava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The renormalization group flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Hořava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.
Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
Giulio
G
D'Odorico
Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
Frank
F
Saueressig
Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands.
Marrit
M
Schutten