Non-perturbative news from the conformal window

Abstract

Dynamical symmetry breaking plays a crucial role in mass and scale generation. In QCD-like theories, its dependence on the number of fermion flavours determines the phase structure and the transition to the conformal regime. In this work, we employ the functional renormalisation group and the generalised flow equation to compute non-perturbative corrections, including momentum dependencies and field invariants essential for an adequate realisation of the global symmetry. As a consequence, the critical gauge coupling required for dynamical chiral symmetry breaking acquires a strong dependence on the number of flavours and increases sharply at $N_f^{\text{crit}}\simeq 7.30$ for $N_c=3$. This establishes a new picture of the conformal phase transition that challenges Miransky/BKT scaling and the existence of walking regimes, favours a first-order quantum phase transition, and points towards a critical region with exotic dynamics and symmetric fermion mass gaps.

32 pages, 7 figures