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One-loop renormalization in a toy model of Horava-Lifshitz gravity

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I will present some recent results on the UV properties of a toy model of Horava-Lifshitz gravity in 2+1 dimensions. In particular, I will illustrate some details of a one-loopcalculation, leading to beta functions for the running couplings. The renormalization group flow obtained in such way shows that Newton's constant is asymptotically free. However, the DeWitt
supermetric approaches its Weyl invariant form with the same speed and the effective interaction coupling of the scalar degree of freedom remains constant along the flow. I will discuss some general lesson that we can learn from these results.