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The standard model is a chiral gauge theory where the gauge fields couple tothe right-hand and the left-hand fermions differently. The standard model isdefined perturbatively and describes all elementary particles (exceptgravitons) very well. However, for a long time, we do not know if we can have anon-perturbative definition of standard model as a Hamiltonian quantummechanical theory. In this paper, we propose a way to give a modified standardmodel (with 48 two-component Weyl fermions) a non-perturbative definition byembedding the modified standard model into a SO(10) chiral gauge theory andthen putting the SO(10) chiral gauge theory on a 3D spatial lattice with acontinuous time. Such a non-perturbatively defined standard model is aHamiltonian quantum theory with a finite-dimensional Hilbert space for a finitespace volume. Using the defining connection between gauge anomalies and thesymmetry-protected topological orders, we show that any chiral gauge theory canbe non-perturbatively defined by putting it on a lattice in the same dimension,as long as the chiral gauge theory is free of all anomalies.

A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model