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Gauge-fermion cartography: From confinement and chiral symmetry breaking to conformality

Florian Goertz1, Álvaro Pastor-Gutiérrez1,2, and Jan M. Pawlowski2,3

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Phys. Rev. D 112, 034029 – Published 26 August, 2025

DOI: https://doi.org/10.1103/7dzj-k6k8

Abstract

We study, for the first time, the interplay between color-confining and chiral symmetry-breaking dynamics in gauge-fermion systems with a general number of flavors and colors. Specifically, we work out the flavor 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 renormalization 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-flavor 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 flavor numbers. We also explore the close-conformal region that displays a walking behavior. Finally, we provide a quantitative estimate for the lower boundary of the conformal Caswell-Banks-Zaks window, with a Nfcrit(Nc=3)=9.60−0.53+0.55. 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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Phys. Rev. D 112, 034029– Published 26 August, 2025
  • Received 9 January 2025
  • Accepted 28 July 2025
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