2013/05/31 by Xiao-Gang Wen · 1 citation
Physics and Astronomy · #hep-lat #cond-mat.str-el #hep-th
paper · pdf · doi:10.1088/0256-307x/30/11/111101
published as Chin. Phys. Lett. (2013) Vol. 30, 111101 · 7 pages, 1 figure, RevTex4. arXiv admin note: text overlap with arXiv:1303.1803
arxiv created 2015/03/13 · arxiv updated 2015/03/16
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 embedding 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 volume. 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.