Pinched geometries in 2D Lorentzian quantum Regge calculus

TL;DR

This paper studies the suppression of pinched geometries in 2D Lorentzian quantum Regge calculus using tensor renormalization group methods, indicating a tendency towards smooth geometries in the continuum limit.

Contribution

It demonstrates that pinched geometries are strongly suppressed across various measures and triangulations, suggesting universality and the emergence of smooth geometries in the model.

Findings

Pinched geometries are strongly suppressed.

Suppression is consistent across different measures.

Results indicate potential emergence of smooth geometries.

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.