2018/11/02 by Astrid Eichhorn, Tim Koslowski, Johannes Lumma +2 · 23 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Degrees of freedom (physics and chemistry) #Formalism (music) #Granularity #Noncommutative and Quantum Gravity Theories #Phase transition #Quantum #Quantum gravity #Quantum many-body systems #Scaling #Tensor (intrinsic definition) #Universality (dynamical systems) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1361-6382/ab2545
published in Classical and Quantum Gravity 36(15), 155007 (IOP Publishing) · 23 pages plus appendix and references
arxiv created 2018/11/02 · openalex created_date 2018/11/09 · openalex publication_date 2019/05/29 · arxiv updated 2020/10/07 · openalex updated_date 2026/08/05
Abstract We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of space. The latter are associated to rank d tensors of size N . We search for a universal large N scaling limit in a rank-3 model with real tensors that could be linked to a transition between the two phases. We extend the conceptual development and practical implementation of the flow equation for the pregeometric setting. This provides a pregeometric ‘coarse-graining’ by going from many microscopic to few effective degrees of freedom by lowering N . We discover several candidates for fixed points of this coarse graining procedure, and specifically explore the impact of a novel class of interactions allowed in the real rank-3 model. In particular, we explain how most universality classes feature dimensional reduction, while one candidate, involving a tetrahedral interaction, might potentially be of relevance for three-dimensional quantum gravity.