Generalized uncertainty principle, quantum gravity and Hořava-Lifshitz gravity

We investigate a close connection between generalized uncertainty principle (GUP) and deformed Hořava-Lifshitz (HL) gravity. The GUP commutation relations correspond to the UV-quantum theory, while the canonical commutation relations represent the IR-quantum theory. Inspired by this UV/IR quantum mechanics, we obtain the GUP-corrected graviton propagator by introducing UV-momentum pi=p0i(1+βp02) and compare this with tensor propagators in the HL gravity. Two are the same up to p04-order.