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

TL;DR

This paper maps the phase structure of gauge-fermion theories, revealing how confinement, chiral symmetry breaking, and conformality depend on flavor number, using a novel functional renormalisation group approach.

Contribution

It introduces a new approximation scheme within the functional renormalisation group framework to study the phase diagram of gauge-fermion systems across different flavor counts.

Findings

Identifies a phase with locked confinement and chiral symmetry breaking at intermediate flavors.

Provides a quantitative estimate for the lower boundary of the conformal window at $N_f^{crit}=9.60^{+0.55}_{-0.53}$ for $N_c=3$.

Connects QCD-like and conformal regimes, matching lattice data and perturbative predictions.

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.