Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

We apply the BMHV scheme for non-anticommuting $\gamma_5$ to an abelian chiral gauge theory at two-loop level. As our main result, we determine full structure of symmetry-restoring counterterms up These turn out have same as one-loop level and a simple interpretation in terms restoration well-known Ward identities. In addition, show that ultraviolet divergences cannot be canceled completely by generated field parameter renormalization, needed UV divergent evanescent counterterms. The paper establishes methodology based on quantum action principle direct computations Slavnov-Taylor identity breakings. method will applicable nonabelian theories.