Gapped Chiral Fermions

Abstract

In principle, there is no obstacle to gapping fermions preserving any global symmetry that does not suffer a 't Hooft anomaly. In practice, preserving a symmetry that is realised on fermions in a chiral manner necessitates some dynamics beyond simple quadratic mass terms. We show how this can be achieved using familiar results about supersymmetric gauge theories and, in particular, the phenomenon of confinement without chiral symmetry breaking. We present simple models that gap fermions while preserving a symmetry group under which they transform in chiral representations. For example, we show how to gap a collection of 4d fermions that carry the quantum numbers of one generation of the Standard Model, but without breaking electroweak symmetry. We further show how to gap fermions in groups of 16 while preserving certain discrete symmetries that exhibit a mod 16 anomaly.

21 pages. v2: references added

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• Asymptotic Accelerated Expansion in String Theory and the Swampland
• Anomalies and symmetric mass generation for Kaehler-Dirac fermions
• Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
• 't Hooft anomalies for staggered fermions
• Chiral Lattice Fermions From Staggered Fields
• Unwinding Fermionic SPT Phases: Supersymmetry Extension
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• Fermi Surface Symmetric Mass Generation
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Dispersive constraints on fermion masses
• A no-go result for implementing chiral symmetries by locality-preserving unitaries in a 3 dimensional Hamiltonian lattice model of fermions
• CT or P Problem and Symmetric Gapped Fermion Solution
• Induced topological gravity and anomaly inflow from Kaehler-Dirac fermions in odd dimensions
• Lattice Regularization of Reduced Kähler-Dirac Fermions and Connections to Chiral Fermions
• Flavor Hierarchy from Smooth Confinement