Chiral gauge theory
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.Lattice regularizations suffer from fermion doublings leading to a loss of chirality.
