3 years ago

Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz.

Aleksandr Pinzul, Fedele Lizzi

We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed Laplace operator, this model demonstrates quite non-trivial behaviour: the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with the similar property, the so-called Horava-Lifshitz model, our construction does not have any preferred direction. The dimension flow is rather achieved by a rearrangement of the degrees of freedom. In this respect the number of dimensions is deceptive. Some physical consequences are discussed.

Publisher URL: http://arxiv.org/abs/1711.01461

DOI: arXiv:1711.01461v1

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