1305.1045 (Xiao-Gang Wen)

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

Xiao-Gang Wen

The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of standard model as a Hamiltonian quantum mechanical theory. In this paper, we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embeding the modified standard model into a SO(10) chiral gauge theory and then putting the SO(10) chiral gauge theory on a 3D spatial lattice with a continuous time. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volum. Using the defining connection between gauge anomalies and the symmetry-protected topological orders, we show that any chiral gauge theory can be 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.

View original: http://arxiv.org/abs/1305.1045