Gauge Invariance and Finite Counterterms in Chiral Gauge Theories

Understand

We derive the finite one-loop counterterm required to restore the Ward Identities broken by the regularization scheme in chiral gauge theories.

• Our result is an analytic expression applicable to a wide class of regularizations satisfying a few general properties.
• We adopt the background field method, which ensures background gauge invariance in the quantized theory, and focus on renormalizable chiral theories with arbitrary gauge group and fermions in general representations.
• Our approach can be extended to theories involving scalars, such as the Standard Model, or to non-renormalizable theories, such as the SMEFT.