Advances at the γ₅-Frontier

These proceedings discuss the current progress of the no-compromise approach to the dimensional renormalization of chiral gauge theories in the context of the BMHV scheme with non-anticommuting γ₅. Despite spuriously breaking BRST-invariance in intermediate steps, it is the only scheme which handles the well-known γ₅-problem mathematically consistently. We begin with a brief motivation, followed by an exposition of our methodology. Specifically, we illustrate the symmetry restoration procedure to obtain the required symmetry-restoring counterterms and provide insights into our computational setups, including recent developments. Building up on this, we present recent results and advances for the multi-loop renormalization of Abelian and non-Abelian chiral gauge theories, before concluding this article with a discussion on prospective implementations of the BMHV regularization in SM-like models.