A Non-Perturbative Definition of the Standard Models

Abstract

The Standard Models contain chiral fermions coupled to gauge theories. It has been a long-standing problem to give such gauged chiral fermion theories a quantum non-perturbative definition. By classification of quantum anomalies and symmetric invertible topological orders via a mathematical cobordism theorem for differentiable and triangulable manifolds, and the existence of symmetric gapped boundary for the trivial symmetric invertible topological orders, we propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined on a 3+1D lattice, and subsequently dynamically gauged to be a Spin(10) chiral gauge theory. As a result, the Standard Models from the 16n-chiral fermion SO(10) Grand Unification can be defined non-perturbatively via a 3+1D local lattice model of bosons or qubits. Furthermore, we propose that Standard Models from the 15n-chiral fermion SU(5) Grand Unification can also be realized by a 3+1D local lattice model of fermions.

arXiv comment24 pages. Two columns. v3: Refinement with detailed discussions. Appendices include viewpoints from perturbative local anomalies and non-perturbative global anomalies (e.g. arXiv:1810.00844, SU(2) = Spin(3) $\subset$ Spin(10)), and co/bordism theories (e.g. ${\Omega }_D^{(\mathrm{Spin}(D)\times \mathrm{Spin}(10))/{\mathbb{Z}}_2^f}$)

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