Spectral dimension of Horava-Snyder spacetime and the $AdS_2\times S^2$ momentum space

TL;DR

This paper explores the connection between Lifshitz-type quantum gravity at z=3 and a curved momentum space with topology of AdS2×S2, linking non-commutative geometry to quantum spacetime models.

Contribution

It establishes an equivalence between the UV regime of Horava-Lifshitz gravity and Snyder's non-commutative spacetime through the topology of the momentum space.

Findings

UV regime at z=3 corresponds to AdS2×S2 momentum space

Curved momentum space relates to non-commutative spacetime

Suggests an equivalence between Horava-Lifshitz and Snyder's theories

Abstract

We show that the UV-regime at the Lifshitz point $z=3$ is equivalent to work with a momenta manifold whose topology is the same as that of an $AdS_2\times S^2$ space. According to Snyder's theory, curved momentum space is related to non-commutative quantized spacetime. In this sense, our analysis suggests an equivalence between Horava-Lifshitz and Snyder's theory.