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

Understand

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.