Chiral gauge theories and non-abelian analogues of axions

The axion particle may or not exist, but the field can be used, as shown here, in an explicitly local formulation of a chiral U(1) gauge theory with both classical and quantum invariance. Nonabelian analogues fields, which have recently been introduced, together their special symmetries, similar construction nonabelian theories. As known cases, symmetry is broken boson acquires mass by swallowing axions are therefore physical this construction.