On the phase structure of massless many-flavour QCD with staggered fermions

When the number of massless fermions exceeds a critical value $N_f^{\ast }$, QCD enters the conformal window and becomes chirally symmetric already in the vacuum. Determining $N_f^{\ast }$ from lattice simulations is challenging, since calculations are performed at finite lattice spacing, quark mass, and temporal lattice size, where both a thermal transition and an unphysical bulk transition obscure the conformal behaviour. In this work, we present results on the chiral phase boundaries in the bare lattice parameter space $(N_{\tau },\beta ,am,N_f)$ of unimproved staggered fermions. Our analysis indicates that the chiral transition in continuum QCD is of second order for all $N_f$ up to the onset of the conformal window. By systematically studying the thermal chiral transition and its interplay with the bulk transition, we obtain a coherent picture of the lattice phase structure and suggest how the onset of the conformal window can be identified from simulations performed away from the chiral and continuum limits.