Effects of high-order operators in non-relativistic Lifshitz holography

In this paper, we study the effects of high-order operators on the non-relativistic Lifshitz holography in the framework of the Ho\v{r}ava-Lifshitz (HL) theory of gravity, which naturally contains high-order operators in order for the theory to be power-counting renormalizble, and provides an ideal place for such studies. In particular, we show that the Lifshitz space-time is still a solution of the full theory of the HL gravity. The effects of the high-oder operators on the space-time itself is simply to shift the Lifshitz dynamical exponent. However, while in the infrared the asymptotic behavior of a (probe) scalar field near the boundary is similar to that studied in the literature, it gets dramatically modified in the UV limit, because of the presence of the high-order operators in this regime. Then, according to the gauge/gravity duality, this in turn affects the two-point correlation functions.