UV dimensional reduction to two from group valued momenta

TL;DR

This paper introduces a new model of deformed relativistic kinematics using a group manifold as momentum space, revealing a two-scale structure and a running spectral dimension that reduces to two at short distances, relevant for quantum gravity.

Contribution

It proposes a novel group-valued momentum space model with two energy scales and analyzes its geometric and kinematic properties, including spectral dimension behavior.

Findings

Deformed kinematics governed by two energy scales,  and .

Spectral dimension runs to 2 at short distances, indicating dimensional reduction.

Model provides insights into quantum gravity phenomenology.

Abstract

We describe a new model of deformed relativistic kinematics based on the group manifold $U(1) \times SU(2)$ as a four-momentum space. We discuss the action of the Lorentz group on such space and and illustrate the deformed composition law for the group-valued momenta. Due to the geometric structure of the group, the deformed kinematics is governed by {\it two} energy scales $\lambda$ and $\kappa$. A relevant feature of the model is that it exhibits a running spectral dimension $d_s$ with the characteristic short distance reduction to $d_s =2$ found in most quantum gravity scenarios.