Anomalies in family unification models from bordism classification

概要

Anomaly cancellation is one of the most fundamental consistency conditions in quantum field theory. In constructing models beyond the Standard Model, one must ensure the absence of anomalies that would render the theory inconsistent. Consequently, anomaly cancellation conditions impose strong constraints on the allowed matter content. Recent developments have made it possible to systematically study not only perturbative anomalies but also the more subtle global anomalies via bordism theory. This perspective has led to a deeper understanding of anomalies and their implications for model building. In this talk, I will discuss anomalies in family unification models, which provide a natural explanation for the three generations of quarks and leptons. We identify the relevant bordism groups that classify possible anomalies in these models and show that no global anomalies arise. We also revisit earlier studies of perturbative anomalies in these models dating back to the 1980s. This talk is based on joint work with Tsubasa Sugeno (Tohoku University), arXiv:2604.04393.

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