Pinched geometries in 2D Lorentzian quantum Regge calculus
Abstract
We investigate pinched geometries in a two-dimensional Lorentzian model of quantum Regge calculus (QRC) using the tensor renormalization group (TRG) 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.
Keywords
Cite
@article{arxiv.2510.22596,
title = {Pinched geometries in 2D Lorentzian quantum Regge calculus},
author = {Yoshiyasu Ito and Daisuke Kadoh and Yuki Sato},
journal= {arXiv preprint arXiv:2510.22596},
year = {2026}
}
Comments
18 pages, 27 figures; v2: corresponds to the version accepted in Phys. Rev. D, including the Data Availability Statement, 19 pages