Nature of the zero-temperature phase transition at the lower edge of the conformal window

Determine the order and mechanism of the zero-temperature quantum phase transition between the infrared-conformal phase and the chirally broken phase in asymptotically free non-Abelian gauge theories with massless fermions, clarifying whether the transition is infinite-order (Berezinskii–Kosterlitz–Thouless type), weak first-order, or of another character.

Background

Asymptotically free non-Abelian gauge theories with sufficiently many massless fermion flavors can exhibit an infrared fixed point, giving rise to an infrared-conformal phase over a range of flavor number known as the conformal window. Below the upper bound set by asymptotic freedom, the theories transition from an infrared-conformal phase to a chirally broken, confining phase as the number of flavors decreases.

The character of the zero-temperature quantum phase transition at the lower edge of the conformal window is a central theoretical issue with direct implications for walking dynamics, scale separation, and the emergence of light scalars in near-conformal theories relevant to composite Higgs and related BSM scenarios. Establishing the precise nature of this transition remains challenging due to strong coupling and large characteristic length scales, and competing conjectures (infinite-order versus weak first-order) motivate both analytical and lattice investigations.