Lifshitz dynamics in the UV

Lifshitz field theories are non-relativistic theories which enjoy an anisotropic scaling between space and time driven by an exponent z. Their applications span many fields in physics, from condensed matter physics, non-relativistic holography or quantum gravity. We study the quantum dynamics of these kind of theories at the one-loop level in curved space-time, deriving all the machinery needed to perform a zeta function regularization of the effective action and explicitly computing the Heat Kernel of a generalized Lifshitz operator. We also address the issue of anisotropic Weyl anomalies for arbitrary space-time dimension D+1 satisfying the constraint z>D.