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A Non-Perturbative Definition of the Standard Models
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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.
Forward citations
Cited by 4 Pith papers
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The absence of global anomalies of CP symmetry
Gauged CP symmetry in four dimensions introduces no new global anomalies for connected, simply-connected gauge groups; the standard model matter content is anomaly-free under a gauged CP.
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Topological Responses of the Standard Model Gauge Group
An infinite family of baryon-minus-lepton-like symmetries yields fractional topological responses that can uniquely distinguish all four Standard Model gauge group variants for n ≥ 7 (except 10, 12, 15, 30).
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Quantum Many-Body Lattice C-R-T Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation
Using lattice symmetry fractionalization, the paper shows that 8 staggered Majorana or 4 staggered Dirac fermion copies can always be gapped symmetrically, with explicit stabilizer interactions.
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To Break or Not to Break: A Review of a No-Go Theorem on Chiral Symmetry Breaking in QCD-like Theories
A review showing that if a QCD-like theory with enough massless flavors is fully color-screened in the infrared, then chiral symmetry must be spontaneously broken.
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