String-net liquid

Overview

The string-net model is said to demonstrate how photons, electrons, and U(1) gauge charge can arise, along with masses that are small but not zero relative to the Planck mass, and it suggests that leptons, quarks, and gluons could be modeled in a similar fashion. This means string-net condensation offers a single origin for photons and electrons, or more broadly for gauge bosons and fermions, and can be seen as a way to explain light and the electron.

Still, the model fails to address the chiral coupling between fermions and SU(2) gauge bosons found in the Standard Model. When strings are labeled by positive integers, string-nets match the spin networks used in loop quantum gravity. This connection led to the idea that loop quantum gravity's spin networks could produce the Standard Model through this mechanism, including Fermi statistics and gauge interactions. No strict derivation from loop quantum gravity's spin networks to Levin and Wen's spin lattice has been completed yet, but the effort is called quantum graphity.

A later paper by Tomasz Konopka, Fotini Markopoulou, and Simone Severini argued that certain similarities to spin networks (though not an exact equivalence) can yield U(1) gauge charge and electrons in the string-net framework.