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Dimensional deception from noncommutative tori: An alternative to the Horava-Lifshitz model

Fedele Lizzi1,2,3,* and Aleksandr Pinzul4,5,†

  • 1INFN, Sezione di Napoli, Complesso Univ. Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
  • 2Dipartimento di Fisica “E. Pancini,” Università di Napoli “Federico II”, Complesso Univ. Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
  • 3Departament de Física Quàntica i Astrofísica and Institut de Cíencies del Cosmos (ICCUB), Universitat de Barcelona, Martíi Franqués 1, 08028 Barcelona, Spain
  • 4Universidade de Brasília Instituto de Física CEP:70910-900, Brasília, DF, Brazil
  • 5International Center of Physics C.P. 04667, CEP:70910-900, Brasilia, DF, Brazil

  • *fedele.lizzi@na.infn.it
  • †apinzul@unb.br
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Phys. Rev. D 96, 126013 – Published 21 December, 2017

DOI: https://doi.org/10.1103/PhysRevD.96.126013

Abstract

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 nontrivial behavior: the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with a 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.

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Phys. Rev. D 96, 126013– Published 21 December, 2017
  • Received 11 November 2017

© 2017 American Physical Society

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