An SU(12)-based model unifies quark color-flavor and lepton flavor, generates Yukawas via instantons, solves strong CP with massless quarks, implements a flavored seesaw, and stabilizes the proton via a discrete gauge symmetry X = B - 3(L_i + L_j - L_k).
Coupling a Cosmic String to a TQFT
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Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
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Quark-Lepton Color-Flavor Unification
An SU(12)-based model unifies quark color-flavor and lepton flavor, generates Yukawas via instantons, solves strong CP with massless quarks, implements a flavored seesaw, and stabilizes the proton via a discrete gauge symmetry X = B - 3(L_i + L_j - L_k).
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Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
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ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.