Generalized uncertainty principle, quantum gravity and Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper explores the connection between the generalized uncertainty principle and Hořava-Lifshitz gravity, showing that GUP corrections align with tensor propagators in HL gravity up to fourth order in momentum.

Contribution

It establishes a link between GUP and HL gravity by deriving a GUP-corrected graviton propagator and comparing it with HL gravity tensor propagators.

Findings

GUP modifies the graviton propagator at high energies.

GUP-corrected propagator matches HL gravity tensor propagator up to p_0^4 order.

Provides insight into UV/IR quantum gravity relations.

Abstract

We investigate a close connection between generalized uncertainty principle (GUP) and deformed Ho\v{r}ava-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 $p_i=p_{0i}(1+\beta p_{0}^2)$ and compare this with tensor propagators in the HL gravity. Two are the same up to $p_0^4$-order.