Spacetime Quasicrystals

[2601.07769] Spacetime Quasicrystals Support arXiv on Cornell Giving Day! We're celebrating 35 years of open science - with YOUR support! Your generosity has helped arXiv thrive for three and a half decades. Give today to help keep science open for ALL for many years to come. Donate! --> High Energy Physics - Theory arXiv:2601.07769 (hep-th) [Submitted on 12 Jan 2026 ( v1 ), last revised 12 Feb 2026 (this version, v2)] Title: Spacetime Quasicrystals Authors: Latham Boyle , Sotirios Mygdalas View a PDF of the paper titled Spacetime Quasicrystals, by Latham Boyle and Sotirios Mygdalas View PDF HTML (experimental) Abstract: Self-similar quasicrystals (like the famous Penrose and Ammann-Beenker tilings) are exceptional geometric structures in which long-range order, quasiperiodicity, non-crystallographic orientational symmetry, and discrete scale invariance are tightly interwoven in a beautiful way. In this paper, we show how such structures may be generalized from Euclidean space to Minkowski spacetime. We construct the first examples of such Lorentzian quasicrystals (the spacetime analogues of the Penrose or Ammann-Beenker tilings), and point out key novel features of these structures (compared to their Euclidean cousins). We end with some (speculative) ideas about how such spacetime quasicrystals might relate to reality. This includes an intriguing scenario in which our infinite $(3+1)$D universe is embedded (like one of our spacetime quasicrystal examples) in a particularly symmetric $(9+1)$D torus $T^{9,1}$ (which was previously found to yield the most symmetric toroidal compactification of the superstring). We suggest how this picture might help explain the mysterious seesaw relationship $M_{\rm Pl}M_{\rm vac}\approx M_{\rm EW}^{2}$ between the Planck, vacuum energy, and electroweak scales ($M_{\rm Pl}$, $M_{\rm vac}$, $M_{\rm EW}$). Comments: 34 pages (27+7), 17 figures, 5 tables; v2: minor typos corrected, some figures/captions got updated, more references and acknowledgements added Subjects: High Energy Physics - Theory (hep-th) ; General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph); Metric Geometry (math.MG) Cite as: arXiv:2601.07769 [hep-th] (or arXiv:2601.07769v2 [hep-th] for this version) https://doi.org/10.48550/arXiv.2601.07769 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sotirios Mygdalas [ view email ] [v1] Mon, 12 Jan 2026 17:50:44 UTC (8,218 KB) [v2] Thu, 12 Feb 2026 17:03:34 UTC (7,868 KB) Full-text links: Access Paper: View a PDF of the paper titled Spacetime Quasicrystals, by Latham Boyle and Sotirios Mygdalas View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2026-01 Change to browse by: gr-qc hep-ph math math-ph math.MG math.MP References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) Links to Code Toggle Papers with Code ( What is Papers with Code? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? )