Chiral gauge theory

Gauge theory where some left-handed and right-handed Weyl fermions have different charges

In quantum field theory, a chiral gauge theory is a quantum field theory with charged chiral fermions. For instance, the Standard Model is a chiral gauge theory. For topological reasons, chiral charged fermions cannot be given a mass without breaking the gauge symmetry, which will lead to inconsistencies unlike a global symmetry. It is notoriously difficult to construct a chiral gauge theory from a theory which does not already contain chiral fields at the fundamental level. A consistent chiral gauge theory must have no gauge anomaly. Almost by necessity, regulators will have to break the gauge symmetry. This is responsible for gauge anomalies in the first place.

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