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Pinched geometries in 2D Lorentzian quantum Regge calculus

Yoshiyasu Ito1,*, Daisuke Kadoh2,†, and Yuki Sato3,4,‡

  • 1Market Finance Department, The Ogaki Kyoritsu Bank, Ltd. 3-98 Kuruwamachi, Ogaki-shi, Gifu 502-0887, Japan
  • 2Institute for Mathematical Informatics, Meiji Gakuin University Yokohama-shi, Kanagawa 244-8539, Japan
  • 3Department of Mechanical and System Engineering, University of Fukui 3-9-1 Bunkyo, Fukui-shi, Fukui 910-8507, Japan
  • 4Department of Physics, Nagoya University Chikusaku, Nagoya-shi, Aichi, 464-8602, Japan

  • *Contact author: ito@eken.phys.nagoya-u.ac.jp
  • †Contact author: kadoh@mi.meijigakuin.ac.jp
  • ‡Contact author: yukisato@u-fukui.ac.jp
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Phys. Rev. D 113, 026015 – Published 21 January, 2026

DOI: https://doi.org/10.1103/lhp8-sdhd

Abstract

We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus using the tensor renormalization group method. A pinched geometry refers to a configuration with an infinitely long temporal extent, even when the total spacetime area is fixed. We examine several choices of integration measures and triangulations to study whether such geometries can dominate in the limit of infinitely many triangles. Our results indicate that pinched geometries are strongly suppressed, and this suppression is observed across different integral measures and triangulations. These results suggest the possible emergence of smooth geometries as well as a sort of universality for infinitely many triangles.

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Tensor network approach to 2D Lorentzian quantum Regge calculus

Yoshiyasu Ito, Daisuke Kadoh, and Yuki Sato
Phys. Rev. D 106, 106004 (2022)

Article Text

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Phys. Rev. D 113, 026015– Published 21 January, 2026
  • Received 1 November 2025
  • Accepted 8 December 2025
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