Un-spectral dimension and quantum spacetime phases

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.

5 pages, 1 figure, version matching that published by Physics Letters B

References in corpus (11)

• Unparticle Physics
• Noncommutative geometry inspired charged black holes
• Non-commutative geometry inspired higher-dimensional charged, black holes
• Fractal properties of quantum spacetime
• Noncommutative Inspired Black Holes in Extra Dimensions
• Trace Anomaly in Quantum Spacetime Manifold
• Scalar modifications to gravity from unparticle effects may be testable
• The decay-time of non-commutative micro-black holes
• Un-graviton corrections to the Schwarzschild black hole
• Un-particle Effective Action
• Differentiating unparticles from extra dimensions via mini black hole thermodynamics

Cited by in corpus (4)

• Regular black holes in UV self-complete quantum gravity
• A noncommutative approach to the cosmological constant problem
• Un-graviton corrections to the Schwarzschild black hole
• Hausdorff dimension of a particle path in a quantum manifold