Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-05-10
Phys.Lett.B695:290-293,2011
Physics
High Energy Physics
High Energy Physics - Theory
5 pages, 1 figure, version matching that published by Physics Letters B
Scientific paper
10.1016/j.physletb.2010.10.041
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.
Nicolini Piero
Spallucci Euro
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