Constraints on RG Flows from Holographic Entanglement Entropy

We examine the RG flow of a candidate c-function, extracted from the holographic entanglement entropy of a strip-shaped region, for theories with broken Lorentz invariance. We clarify the conditions on the geometry that lead to a break-down of monotonic RG flows as is expected for generic Lorentz-violating field theories. Nevertheless we identify a set of simple criteria on the UV behavior of the geometry which guarantee a monotonic c-function. Our analysis can thus be used as a guiding principle for the construction of monotonic RG trajectories, and can also prove useful for excluding possible IR behaviors of the theory.