Un-spectral dimension and quantum spacetime phases

TL;DR

This paper introduces the un-spectral dimension as a new way to measure quantum spacetime using un-particles, revealing different phases of spacetime structure including a semi-classical, Planckian, and Trans-Planckian phase.

Contribution

It proposes the concept of un-spectral dimension and derives a general expression that characterizes various quantum spacetime phases based on un-particle probes.

Findings

Un-spectral dimension depends on un-particle scaling dimension d_U.

At d_U=1, spacetime appears two-dimensional in the Planckian phase.

Trans-Planckian phase indicates a regime where spacetime loses its physical meaning.

Abstract

In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length $\ell$ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on the other side. We introduce the concept of \textit{un-spectral dimension} $\mathbb{D}_U$ of a $d$-dimensional, euclidean (quantum) spacetime, as the spectral dimension measured by an "un-particle" probe. We find a general expression for the un-spectral dimension $\mathbb{D}_U$ labelling different spacetime phases: a semi-classical phase, where ordinary spectral dimension gets contribution from the scaling dimension $d_U$ of the un-particle probe ; a critical "Planckian phase", where four-dimensional spacetime can be effectively considered two-dimensional when $d_U=1$; a "Trans-Planckian phase", which is accessible to un-particle probes only, where spacetime as we currently understand it looses its physical meaning.