Diana L. López Nacir, Francisco D. Mazzitelli, Leonardo G. Trombetta
We consider an interacting Lifshitz field with z=3 in a curved spacetime. We
analyze the renormalizability of the theory for interactions of the form lambda
phi^n, 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 xi (4)R phi^2 does not receive
large quantum corrections xi >> 1.
View original:
http://arxiv.org/abs/1111.1662
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