Loop quantization from a lattice gauge theory perspective

TL;DR

This paper interprets loop quantization through lattice gauge theory, highlighting issues with effective theories and renormalization, and constructs spin foam models without auxiliary structures, revealing key constraints on coupling constants and spectra.

Contribution

It offers a lattice gauge theory perspective on loop quantization, constructing embedded spin foam models independent of auxiliary structures and analyzing their implications.

Findings

Coupling constants must be at UV-attractive fixed points

Kinematics of loop quantization and spin foam models are compatible

Edge contributions to area spectrum are incompatible with models

Abstract

We present an interpretation of loop quantization in the framework of lattice gauge theory. Within this context the lack of appropriate notions of effective theories and renormalization group flow exhibit loop quantization as an incomplete framework. This interpretation includes a construction of embedded spin foam models which does not rely on the choice of any auxiliary structure (e.g. triangulation) and has the following straightforward consequences: (1) The values of the coupling constants need to be those of an UV-attractive fixed point (2) The kinematics of canonical loop quantization and embedded spin foam models are compatible (3) The weights assigned to embedded spin foams are independent of the 2-polyhedron used to regularize the path integral, $|J|_x = |J|_{x'}$ (4) An area spectrum with edge contributions proportional to $l_{\rm PL}^2 (j+1 / 2)$ is not compatible with embedded spin foam models and/or canonical loop quantization