Non-abelian chiral gauge theories on the lattice remain unsolved

Establish a nonperturbative lattice formulation of non-abelian chiral gauge theories that would provide a consistent lattice definition of the Standard Model.

Background

The paper frames the long-standing difficulty of giving a nonperturbative lattice definition of the Standard Model as arising from the challenge of formulating non-abelian chiral gauge theories on the lattice. While abelian chiral gauge theories have a nonperturbative lattice construction, the non-abelian case has resisted solution for decades.

This open problem motivates the broader investigation into generalized Ginsparg–Wilson relations and lattice realizations of fermionic anomalies, which could be relevant to future attempts at constructing chiral gauge theories on the lattice.