A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model 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. We show that the SO(10) chiral gauge theory can be put on a lattice (a 3D spatial lattice with a continuous time) if we allow fermions to interact. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volume. More generally, using the defining connection between gauge anomalies and the symmetry-protected topological orders, one can show that any truly anomaly-free chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension. Introduction: The U (1) × SU (2) × SU (3) standard model 1–6 is the theory which is believed to describe all elementary particles (except gravitons) in nature. However , the standard model was defined only perturbatively initially, via the perturbative expansion of the gauge coupling constant. Even though the perturbative expansion is known to diverge, if we only keep the first a few orders of the perturbative expansion, the standard model produces results that compare very well with experiments. So the " perturbatively defined standard model " (keeping only first a few orders of the perturbation) is a theory of nature. However, the " perturbatively defined standard model " is certainly not a " Hamiltonian quantum theory " (by keeping only a few orders of the perturbation, the probability may not even be conserved). " Hamiltonian quantum theory " is a quantum theory with (1) a finite dimensional Hilbert space for all the states, (2) a local Hamiltonian operator for the time evolution, (3) operators to describe the physical quantities. So far, we do not know if there is a non-perturbatively defined standard model …