Vacuum stability, fixed points, and phases of QED3 at large Nf

We consider three-dimensional quantum electrodynamics in the presence of a Chern-Simons term at level k and Nf flavors, in the limit of large Nf and k with k/Nf fixed. We consider either bosonic or fermionic matter fields, with and without quartic terms at criticality: the resulting theories are critical and tricritical bosonic QED3, Gross-Neveu, and fermionic QED3. For all such theories we compute the effective potentials and the beta functions of classically marginal couplings, at the leading order in the large Nf limit and to all orders in k/Nf and in the couplings. We determine the renormalization group fixed points and discuss the quantum stability of the corresponding vacua. While critical bosonic and fermionic QED3 are always stable conformal field theories, we find that tricritical bosonic and Gross-Neveu QED3 exist as stable conformal field theories only for specific values of k/Nf. Finally, we discuss the phase diagrams of these theories as a function of their relevant deformations.