Ultraviolet Fixed Point in Covariant Loop Quantum Gravity

TL;DR

This paper explores the ultraviolet behavior of covariant Loop Quantum Gravity, identifying a fixed point where the theory simplifies and ambiguities are reduced, offering insights into its continuum limit.

Contribution

It introduces a new approach to summing over complexes in covariant LQG and identifies a candidate fixed point controlling the ultraviolet regime.

Findings

Quantum geometry condenses to small spin configurations.

At the fixed point, the amplitude reduces to a topological theory.

Triangulation ambiguities are reduced to boundary coefficients.

Abstract

We investigate the ultraviolet behavior of 4-dimensional Lorentzian covariant Loop Quantum Gravity (LQG) and address the problem of infinite ambiguities relating to the triangulation dependence of spinfoam amplitudes. We consider the complete LQG amplitude that summing spinfoam amplitudes over 2-complexes. By introducing spin-network stacks and their covariant extension, spinfoam stacks, the summation over complexes is partitioned into distinct families. We demonstrate that the theory exhibits a condensation phenomenon, where quantum geometry condenses to a dominant small spin configuration. We identify a candidate fixed point controlling the ultraviolet (small spin) regime of covariant LQG. At this fix point, the complete LQG amplitude dynamically reduces to a topological theory at leading order, and the infinite ambiguities of triangulation dependence reduces to a finite set of boundary coefficients associated with a finite basis of 3-dimensional boundary blocks. These results provide a definition for the continuum limit of spinfoam theory at the fundamental level.