Lifshitz scalar fields: one loop renormalization in curved backgrounds

TL;DR

This paper investigates the renormalization properties of a Lifshitz scalar field with dynamical critical exponent z=3 in curved spacetime, focusing on how Lorentz violation affects coupling constants and their quantum corrections.

Contribution

It provides a one-loop renormalization analysis of Lifshitz scalar fields in curved backgrounds, highlighting the persistence of Lorentz-violating couplings at low energies.

Findings

Lorentz violating terms induce non-invariant metric couplings.

Couplings to the Ricci scalar are not significantly corrected unless the mass is very low.

The theory remains renormalizable for even polynomial interactions.

Abstract

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.