Lifshitz scalar fields: one loop renormalization in curved backgrounds

D. LOPEZ NACIR; F.D. MAZZITELLI; L. TROMBETTA

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 85 p. 24051 - 24060

1550-7998

We consider an interacting Lifshitz field with z 1⁄4 3 in a curved spacetime. We analyze the renormaliz- ability of the theory for interactions of the form !0n, with arbitrary even n. We compute the running of the coupling constants both in the ultraviolet and infrared regimes. We show that the Lorentz-violating terms generate couplings to the spacetime metric that are not invariant under general coordinate transformations. These couplings are not suppressed by the scale of Lorentz violation and therefore survive at low energies. We point out that in these theories, unless the effective mass of the field is many orders of magnitude below the scale of Lorentz violation, the coupling to the four-dimensional Ricci scalar $ð4ÞR02 does not receive large quantum corrections $ ) 1. We argue that quantum corrections involving spatial derivatives of the lapse function (which appear naturally in the so-called healthy extension of the Hoˇrava-Lifshitz theory of gravity) are not generated unless they are already present in the bare Lagrangian.