# Chiral Fermion Problem and the String Net Model

In Xiao-Gang Wen's book "Quantum Field Theory of Many-Body Systems", he mentions that

(the string-net condensation picture)...has a problem: we do not yet know how to produce the $SU(2)$ part of the standard model due to the chiral fermion problem.

I have been trying to research the chiral fermion problem and its connection to string-net condensation, but I can't find any good resources/descriptions on any sites or articles. A summary or link(s) on what this problem is and how it relates to the string-net model would be greatly appreciated.

Recently, substantial progress has been made to solve the chiral fermion problem, enlighten by the theory of symmetry protected topological (SPT) state. It is realized that the gauge anomaly are actually classified by the SPT orders [Wen, 2013a], and the SPT classification can be reduced by the interaction [Fidkowski, Kitaev, 2009; 2010]. This means under certain conditions, the perturbative gauge anomaly can be removed by the fermion interaction (at the UV cut-off energy scale). Along this line of though, Prof. Wen argued that the SO(10) chiral gauge theory (with $16n$ chiral fermions) is actually anomaly free under interaction. Therefore it has a non-perturbative lattice definition [Wen, 2013b], which can be further formulated as string-net condensation. Because the SO(10) chiral gauge theory is a Grand Unification Theory (GUT) which includes the SM, so this result (if verified) would solve the chiral fermion problem and eventually unify all matters and gauge forces under the string-net condensation framework. There are also several following-up works [Wang, Wen, 2013; You, BenTov, Xu, 2014; You, Xu, 2014] in support of Prof. Wen's result using different approaches.