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arXiv · 2412.12254

Gauge-Fermion Cartography: from confinement and chiral symmetry breaking to conformality

Florian Goertz·Álvaro Pastor-Gutiérrez·Jan M. Pawlowski
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Abstract

We study, for the first time, the interplay between colour-confining and chiral symmetry-breaking dynamics in gauge-fermion systems with a general number of flavours and colours. Specifically, we work out the flavour dependence of the confinement and chiral symmetry breaking scales. We connect the QCD-like regime, in quantitative agreement with lattice data, with the perturbative conformal limit, thereby exploring uncharted region of theory space. This analysis is done within the first-principles functional renormalisation group approach to gauge-fermion systems and is facilitated by a novel approximation scheme introduced here. This novel scheme enables a relatively simple access to the confining dynamics. This allows us to investigate the whole landscape of many-flavour theories and to provide a cartography of their phase structure. In particular, we uncover a novel phase with the locking of confining and chiral dynamics at intermediate flavour numbers. We also explore the close-conformal region that displays a walking behaviour. Finally, we provide a quantitative estimate for the lower boundary of the conformal Caswell-Banks-Zaks window, with a $N^{\rm crit}_f(N_c=3)= 9.60^{+0.55}_{-0.53}$. This work offers a self-consistent framework for charting the landscape of strongly interacting gauge-fermion theories necessary to reliably study strongly coupled extensions of the Standard Model of particle physics.

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Florian Goertz, Álvaro Pastor-Gutiérrez, Jan M. Pawlowski. 2024-12-16. Gauge-Fermion Cartography: from confinement and chiral symmetry breaking to conformality. https://arxiv.org/abs/2412.12254

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