The Pauli Exclusion Principle and SU(2) Versus SO(3) in Loop Quantum Gravity

TL;DR

This paper explores how the Pauli exclusion principle can explain the dominance of j=1 edges in loop quantum gravity, supporting SU(2) as the gauge group over SO(3) for black hole area quantization.

Contribution

It introduces the idea that a Pauli principle in loop quantum gravity can suppress j=1/2 punctures, maintaining SU(2) as the gauge group while resolving area quantization ambiguities.

Findings

j=1 edges dominate black hole area contributions

Pauli principle explains suppression of j=1/2 punctures

SU(2) gauge group remains consistent with observations

Abstract

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that $j=1$ edges of spin-networks dominate in their contribution to black hole areas as opposed to $j=1/2$ which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from $j=1$ punctures rather than $j=1/2$ punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.