Non-abelian Gauge Fields from Defects in Spin-Networks

TL;DR

This paper explores how defects in spin-networks can give rise to emergent gauge fields, including non-abelian ones, potentially linking condensed matter phenomena with quantum gravity and the Standard Model.

Contribution

It proposes that gauge fields, both abelian and non-abelian, can emerge from defects in symmetry-reduced spin-networks, connecting condensed matter, quantum gravity, and particle physics.

Findings

Emergent gauge fields from lattice defects modeled by the Hubbard model.

Spin-networks can describe quantum horizons in loop quantum gravity.

Non-abelian gauge fields may originate from defect dynamics in spin-networks.

Abstract

\emph{Effective} gauge fields arise in the description of the dynamics of defects in lattices of graphene in condensed matter. The interactions between neighboring nodes of a lattice/spin-network are described by the Hubbard model whose effective field theory at long distances is given by the Dirac equation for an \emph{emergent} gauge field. The spin-networks in question can be used to describe the geometry experienced by a non-inertial observer in flat spacetime moving at a constant acceleration in a given direction. We expect such spin-networks to describe the structure of quantum horizons of black holes in loop quantum gravity. We argue that the abelian and non-abelian gauge fields of the Standard Model can be identified with the emergent degrees of freedom required to describe the dynamics of defects in symmetry reduced spin-networks.