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A Lattice Non-Perturbative Definition of an SO(10) Chiral Gauge Theory and Its Induced Standard Model |
| WEN Xiao-Gang |
1Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
2Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA |
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| Cite this article: |
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WEN Xiao-Gang 2013 Chin. Phys. Lett. 30 111101 |
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Abstract 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 the standard model as a Hamiltonian quantum mechanical theory. Here 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 an 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.
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Received: 27 October 2013
Published: 30 November 2013
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| PACS: |
11.15.Ha
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(Lattice gauge theory)
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12.39.Fe
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(Chiral Lagrangians)
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12.10.Dm
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(Unified theories and models of strong and electroweak interactions)
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