In other words, string-net condensation provides a unified origin for photons and electrons (or gauge bosons and fermions).
For strings labeled by the positive integers, string-nets are the spin networks studied in loop quantum gravity.
This has led to the proposal by Levin and Wen,[2] and Smolin, Markopoulou and Konopka[3] that loop quantum gravity's spin networks can give rise to the standard model of particle physics through this mechanism, along with fermi statistics and gauge interactions.
To date, a rigorous derivation from LQG's spin networks to Levin and Wen's spin lattice has yet to be done, but the project to do so is called quantum graphity, and in a more recent paper, Tomasz Konopka, Fotini Markopoulou, Simone Severini argued that there are some similarities to spin networks (but not necessarily an exact equivalence) that gives rise to U(1) gauge charge and electrons in the string net mechanism.
It can be shown that the ground-state of the standard toric code Hamiltonian is an equal-weight superposition of closed-string states.