Charting the landscape of gauge-fermion dynamics

Gauge–fermion quantum field theories are central to our understanding of nature, from QCD to the electroweak sector. Beyond the Standard Model, strongly coupled gauge dynamics offer compelling avenues to address open puzzles. In this talk, I present a cartographic study of gauge–fermion theories across varying numbers of colours and flavours, focusing on the interplay between colour confinement and chiral symmetry breaking. We determine the flavour and colour dependence of the corresponding dynamical scales, providing a unified picture that interpolates between QCD-like regimes—where we recover quantitative agreement with lattice results—and the perturbative conformal limit. The analysis is based on the functional renormalisation group and employs a novel approximation scheme that allows for controlled and flexible access to the non-perturbative dynamics. We further explore the near-conformal regime with walking behaviour and estimate the lower boundary of the Caswell–Banks–Zaks conformal window. This framework enables a self-consistent mapping of the theory space of strongly coupled gauge–fermion systems and yields first-principles results with direct relevance for physics beyond the Standard Model.