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

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>N</a:mi><a:mi>f</a:mi><a:mrow><a:mi>crit</a:mi></a:mrow></a:msubsup><a:mo stretchy="false">(</a:mo><a:msub><a:mi>N</a:mi><a:mi>c</a:mi></a:msub><a:mo>=</a:mo><a:mn>3</a:mn><a:mo stretchy="false">)</a:mo><a:mo>=</a:mo><a:mn>9.6</a:mn><a:msubsup><a:mn>0</a:mn><a:mrow><a:mo>−</a:mo><a:mn>0.53</a:mn></a:mrow><a:mrow><a:mo>+</a:mo><a:mn>0.55</a:mn></a:mrow></a:msubsup></a:math>. 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.