CFTs with $\mathbf{U(m)\times U(n)}$ global symmetry in 3D and the chiral phase transition of QCD

Abstract

Conformal field theories (CFTs) with U(m)\times U(n)U(m)×U(n) global symmetry in d=3d=3 dimensions have been studied for years due to their potential relevance to the chiral phase transition of quantum chromodynamics (QCD). In this work such CFTs are analyzed in d=4-\varepsilond=4−ε and d=3d=3. This includes perturbative computations in the \varepsilonε and large-nn expansions as well as non-perturbative ones with the numerical conformal bootstrap. New perturbative results are presented and a variety of non-perturbative bootstrap bounds are obtained in d=3d=3. Various features of the bounds obtained for large values of nn disappear for low values of nn (keeping m<nm<n fixed), a phenomenon which is attributed to a transition of the corresponding fixed points to the non-unitary regime. Numerous bootstrap bounds are found that are saturated by large-nn results, even in the absence of any features in the bounds. A double scaling limit is also observed, for mm and nn large with m/nm/n fixed, both in perturbation theory as well as in the numerical bootstrap. For the case of two-flavor massless QCD existing bootstrap evidence is reproduced that the chiral phase transition may be second order, albeit associated to a universality class unrelated to the one usually discussed in the \varepsilonε expansion. Similar evidence is found for the case of three-flavor massless QCD, where we observe a pronounced kink.